diff --git "a/raw_rss_feeds/https___arxiv_org_rss_math.xml" "b/raw_rss_feeds/https___arxiv_org_rss_math.xml" --- "a/raw_rss_feeds/https___arxiv_org_rss_math.xml" +++ "b/raw_rss_feeds/https___arxiv_org_rss_math.xml" @@ -7,4680 +7,12 @@ http://www.rssboard.org/rss-specification en-us - Thu, 06 Nov 2025 05:00:13 +0000 + Sat, 08 Nov 2025 05:00:03 +0000 rss-help@arxiv.org - Thu, 06 Nov 2025 00:00:00 -0500 + Sat, 08 Nov 2025 00:00:00 -0500 - Saturday Sunday + Saturday - - Perspectives on the arithmetic nature of the ratios $\zeta(2n + 1)/\pi^{2n+1}$ and $\beta(2n)/\pi^{2n}$ - https://arxiv.org/abs/2511.02843 - arXiv:2511.02843v1 Announce Type: new -Abstract: We investigate the values of the Riemann zeta function at odd integers and the Dirichlet beta function at even integers, by collecting several distinct analytic frameworks converging to these values, thus providing a unifying perspective. Beyond analytic interest, these formulas motivate linear independence conjectures which, if established, would imply the irrationality of the quantities $\zeta(2n + 1)/\pi^{2n+1}$ and $\beta(2n)/\pi^{2n}$ - oai:arXiv.org:2511.02843v1 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Luc Rams\`es Talla Waffo - - - Heisenberg's S-matrix program and Feynman's divergence problem - https://arxiv.org/abs/2511.02847 - arXiv:2511.02847v1 Announce Type: new -Abstract: In the present article, we assume that the first approximation of the scattering operator is given and that it has the logarithmic divergence. This first approximation allows us to construct the so called deviation factor. Using the deviation factor, we regularize all terms of the scattering operator's approximations. The infrared and ultraviolet cases as well as concrete examples are considered. Thus, for a wide range of cases, we provide a positive answer to the well-known problem of J. R. Oppenheimer regarding scattering operators in QED: ``Can the procedure be freed of the expansion in $\varepsilon$ and carried out rigorously?" - oai:arXiv.org:2511.02847v1 - math-ph - hep-th - math.MP - math.SP - quant-ph - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Lev Sakhnovich - - - Isomorphisms of $\Spin\left( \frac{1}{2}\right) $ to $\SU(1,1)-\mbox{Boson}$: Universal Enveloping and Kangni-type Transformation - https://arxiv.org/abs/2511.02855 - arXiv:2511.02855v1 Announce Type: new -Abstract: In this study we investigate the nexus between the $\Spin (\frac12)$ and the $\SU(1,1)$-quasi boson Lie structure and reveal related properties as well as some decomposition of spin particles. We show that the $\SU(1,1)$-quasi boson has a left invariant Haar measure and we ascertain its spherical Fourier transformation. We finally show that this spherical Fourier transformation of type delta is a Kangni-type transform when the Planck's constant, $\hbar=1$. - oai:arXiv.org:2511.02855v1 - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Francis Atta Howard, Kinvi Kangni - - - Non-Archimedean Kelvin Transformation - https://arxiv.org/abs/2511.02858 - arXiv:2511.02858v1 Announce Type: new -Abstract: We introduce and study an analog of the Kelvin transformation connected with the Vladimirov-Taibleson operator acting on real- or complex-valued functions on a space $K^n$ over a non-Archimedean local field $K$. - oai:arXiv.org:2511.02858v1 - math.NT - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Alexandra V. Antoniouk, Anatoly N. Kochubei - - - Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems - https://arxiv.org/abs/2511.02867 - arXiv:2511.02867v1 Announce Type: new -Abstract: We study the behavior of a probability measure near the bottom of its support in terms of time averaged quotients of its Laplace transform. We discuss how our results are connected to both rank-one perturbation theory as well as renewal theory. We further apply our results in order to derive criteria for the existence and non-existence of ground states for a finite dimensional quantum system coupled to a bosonic field. - oai:arXiv.org:2511.02867v1 - math-ph - math.FA - math.MP - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Benjamin Hinrichs, Steffen Polzer - - - Jensen's Functional Equation on Involution-Generated Groups: An ($\mathrm{SR}_2$) Criterion and Applications - https://arxiv.org/abs/2511.02870 - arXiv:2511.02870v1 Announce Type: new -Abstract: We study the Jensen functional equations on a group $G$ with values in an abelian group $H$: \begin{align} \tag{J1}\label{eq:J1} f(xy)+f(xy^{-1})&=2f(x)\qquad(\forall\,x,y\in G),\\ \tag{J2}\label{eq:J2} f(xy)+f(x^{-1}y)&=2f(y)\qquad(\forall\,x,y\in G), \end{align} with the normalization $f(e)=0.$ Building on techniques for the symmetric groups $S_n$, we isolate a structural criterion on $G$ -- phrased purely in terms of involutions and square roots -- under which every solution to \eqref{eq:J1} must also satisfy \eqref{eq:J2} and is automatically a group homomorphism. Our new criterion, denoted $(\mathrm{SR}_2)$, implies that $S_1(G,H) = S_{1,2}(G,H) = \mathrm{Hom}(G,H)$, applies to many reflection--generated groups and, in particular, recovers the full solution on $S_n.$ Furthermore, we give a transparent description of the solution space in terms of the abelianization $G/[G,G],$ and we treat dihedral groups $D_m$ in detail, separating the cases $m$ odd and even. The approach is independent of division by 2 in $H$ and complements the classical complex-valued theory that reduces \eqref{eq:J1} to functions on $G/[G,[G,G]].$ - oai:arXiv.org:2511.02870v1 - math.GR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dang Vo Phuc - - - Curvature of high-dimensional data - https://arxiv.org/abs/2511.02873 - arXiv:2511.02873v1 Announce Type: new -Abstract: We consider the problem of estimating curvature where the data can be viewed as a noisy sample from an underlying manifold. For manifolds of dimension greater than one there are multiple definitions of local curvature, each suggesting a different estimation process for a given data set. Recently, there has been progress in proving that estimates of ``local point cloud curvature" converge to the related smooth notion of local curvature as the density of the point cloud approaches infinity. Herein we investigate practical limitations of such convergence theorems and discuss the significant impact of bias in such estimates as reported in recent literature. We provide theoretical arguments for the fact that bias increases drastically in higher dimensions, so much so that in high dimensions, the probability that a naive curvature estimate lies in a small interval near the true curvature could be near zero. We present a probabilistic framework that enables the construction of more accurate estimators of curvature for arbitrary noise models. The efficacy of our technique is supported with experiments on spheres of dimension as large as twelve. - oai:arXiv.org:2511.02873v1 - math.ST - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jiayi Chen, Mohammad Javad Latifi Jebelli, Daniel N. Rockmore - - - Asymptotic analysis of a stochastic SVEIS epidemic model using Black-Karasinski process - https://arxiv.org/abs/2511.02882 - arXiv:2511.02882v1 Announce Type: new -Abstract: In this paper, we present a stochastic SVEIS epidemic model perturbed by a Black-Karasinski process. Using a Lyapunov functional approach, we derive a sufficient condition, Rs0>1 for the existence of a stationary distribution, which indicates disease persistence. Additionally, we theoretically demonstrate that the disease will die out at an exponential rate if Re0<1 . Our results show that random fluctuations will facilitate disease outbreak. - oai:arXiv.org:2511.02882v1 - math.PR - q-bio.PE - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-sa/4.0/ - Lahcen Khammich, Driss Kiouach - - - An identity involving counts of binary matrices - https://arxiv.org/abs/2511.02883 - arXiv:2511.02883v1 Announce Type: new -Abstract: In this paper, we prove the proposition shown below and explore some of its consequences. For a sequence $p=(p_1,p_2,\dots)$ of non-negative integers, set $|p| = \sum_{i\geq 1} p_i$ and let $[p] = (\#\{j: p_j=i\})_{i\geq 1}$ count the number of occurrences of $i\geq 1$ in $p$, so that $|[p]|$ is the number of non-zero elements in $p$. For $p\in \mathbb N_0^\infty$ and $x\in \mathbb R$, we write $p!$ and $x^{\underline{p}}$ for the product of factorials $\prod_{i\geq 1}p_i!$ and of falling factorials $\prod_{i\geq 1} x^{\underline{p_i}}$, respectively. If $p$ is an integer partition of $m$, i.e., if $|p|=m$ and $p_1\geq p_2 \geq \dots$, we write $p \vdash m$. Given two integer partitions $p$ and $q$ of $m$, let $N(p,q)$ denote the number of $|[p]|\times |[q]|$ binary matrices whose row-and column-sums equal $p$ and $q$, respectively (for $m=0$, this number is to be interpreted as one). - Proposition: For $q \vdash m$ and $x\in \mathbb R$, we have $$\sum_{p \vdash m} \frac{x^{\underline{|[p]|}}}{[p]!} N(p,q) \quad=\quad \frac{x^{\underline{q}}}{q!}.$$ - oai:arXiv.org:2511.02883v1 - math.CO - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Hannes Leeb - - - Open problems of the 33rd Workshop on Cycles and Colourings - https://arxiv.org/abs/2511.02892 - arXiv:2511.02892v1 Announce Type: new -Abstract: Since its beginnings, every Cycles and Colourings workshop holds one or two open problem sessions; this document contains the problems (together with notes regarding the current state of the art and related bibliography) presented by participants of the 33rd edition of the workshop which took place in Nov\'y Smokovec, Slovakia during August 31st - September 5th, 2025 (see the workshop webpage https://candc.upjs.sk). - oai:arXiv.org:2511.02892v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - J\'anos Bar\'at, Zden\v{e}k Dvo\v{r}\'ak, Penny Haxell, Franti\v{s}ek Kardo\v{s}, Borut Lu\v{z}ar, Alfr\'ed Onderko, Jozef Rajn\'ik, Roman Sot\'ak, Nikolay Ulyanov - - - Representations of loop groups as factorization module categories - https://arxiv.org/abs/2511.02916 - arXiv:2511.02916v1 Announce Type: new -Abstract: We show that the (2-)category of categorical representations of the loop group embeds fully faithfully into the (2-)category of factorization module categories with respect to the affine Grassmannian. - oai:arXiv.org:2511.02916v1 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Lin Chen, Yuchen Fu, Dennis Gaitsgory, David Yang - - - Long-term behaviour of symmetric partitioned linear multistep methods II. Invariants error analysis for some nonlinear dispersive wave models - https://arxiv.org/abs/2511.02921 - arXiv:2511.02921v1 Announce Type: new -Abstract: In this paper, the use of partitioned linear multistep methods (PLMM) as time integrators for the numerical approximation of some partial differential equations (pdes) is studied. We consider the periodic initial-value problem of two nonlinear dispersive wave models as case studies. From the spatial discretization with pseudospectral methods, the theory developed for PLMMs by the authors in a previous companion paper is applied to analyze the time integration with PLMMs of the semidiscrete equations when approximating solitary wave solutions. The results are illustrated with some numerical experiments. In addition, a computational study is performed in an exploratory fashion to analyze the extension of the results to the approximation of more general localized solutions. - oai:arXiv.org:2511.02921v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Bego\~na Cano, Angel Dur\'an, Melqu\'iades Rodr\'iguez - - - Boltzmann-Grad limit for the inelastic Lorentz gas: Part I. Existence, uniqueness, and rigorous derivation via weak convergence - https://arxiv.org/abs/2511.02934 - arXiv:2511.02934v1 Announce Type: new -Abstract: In this paper we provide a rigorous derivation of the inelastic linear Boltzmann equation, in the Boltzmann-Grad limit, from a dissipative, random, Lorentz gas in arbitrary dimensions d $\geq$ 2. Specifically, we consider a microscopic particle system where scatterers are randomly distributed according to a Poisson process, and a tagged light particle undergoes inelastic collisions with the scatterers following a reflection law characterized by a fixed restitution coefficient. We establish the existence and uniqueness of weak solutions to the inelastic linear Boltzmann equation within the class of non-negative Radon measures, assuming that the initial data has a finite exponential moment. We first show that the forward dynamics of the dissipative particle system is globally defined almost surely and then prove the weak$-*$ convergence of the microscopic solution towards the weak solutions of the inelastic linear Boltzmann equation, providing an explicit rate of convergence. Furthermore, under the same initial data assumptions, we prove the existence of strong solutions to the inelastic linear Boltzmann equation, constructed via a series representation of the solutions. - oai:arXiv.org:2511.02934v1 - math-ph - math.AP - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Th\'eophile Dolmaire, Alessia Nota - - - Matroid adjoints and the minimum rank of zero-nonzero matrix patterns - https://arxiv.org/abs/2511.02935 - arXiv:2511.02935v1 Announce Type: new -Abstract: The problem of finding the minimum rank of a matrix with a given zero-nonzero pattern has been generalized to a class of matroids associated to the pattern. The fundamental lower bound known as the triangle number still holds in this generalized setting. But the matroid minimum rank of a pattern need not match that of its transpose. - We associate to each pattern $X$ a lattice $L(X)$. We define the fundamental pattern of a matroid $M$ to be the complement of its hyperplane-point incidence pattern and note that when $X$ is the fundamental pattern of $M$, the lattice of flats of $M$ is $L(X)$. We then prove that, for every pattern $X$, the dual lattice of $L(X)$ is isomorphic to $L(X^T)$. - We show that a matroid $M'$ of the same rank as $M$ is an adjoint of $M$ if and only if $M'$ is associated with the transpose of the fundamental pattern of $M$. Our main result ties together the notion of a matroid adjoint with the phenomenon of a gap between the triangle number $k$ and the matroid minimum rank of a pattern. Namely, we show that, if any matroid of rank $k$ associated with a pattern has an adjoint, then there is no such gap for the pattern's transpose. - We show that the matroid of minimum rank associated with the fundamental pattern is unique. Using this, we prove that the matrix minimum rank of the fundamental pattern of a matroid over different fields depends on the representability of the matroid over those fields. This allows us to recover and improve upon a construction of Berman et al. We also give a smaller example than any previously known of a pattern with a matroid minimum rank smaller than its matrix minimum rank over every field. Finally, we establish that, for the fundamental pattern, a converse holds to our main result. In particular, a matroid with fundamental pattern $X$ has an adjoint if and only if the matroid minimum rank of $X^T$ is equal to its triangle number. - oai:arXiv.org:2511.02935v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Louis Deaett, Kevin Grace - - - Automorphisms with growing generators - https://arxiv.org/abs/2511.02941 - arXiv:2511.02941v1 Announce Type: new -Abstract: We prove global existence and uniqueness of Heisenberg dynamics on the quasi-local algebra of an extended quantum lattice system for spatially growing generators. Existing results assume that the local terms of the generator decay fast enough and are bounded uniformly in space and time. We show, in analogy to global existence results for first order ODEs, that global existence and uniqueness still hold true if the local terms grow at most linearly in space. Moreover, we obtain Lieb-Robinson bounds with exponential light cones for the generated dynamics. - For the proof, we mainly assume Lieb-Robinson bounds with linear light cones for dynamics generated by uniformly bounded local terms. These are known to hold for example if the local terms are exponentially localized. - oai:arXiv.org:2511.02941v1 - math-ph - math.MP - quant-ph - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Stefan Teufel, Marius Wesle, Tom Wessel - - - Ignorance as an excuse, formally - https://arxiv.org/abs/2511.02942 - arXiv:2511.02942v1 Announce Type: new -Abstract: There is a lively debate in the current literature on epistemology on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never thought about or considered as true a proposition $p$. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis has been provided for ignorance as an excuse. We fill this gap by proposing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which excusable ignorance is expressed as a primitive modality. This logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, to consider the conditions of a possible change of an agent's ignorance, we will extend the setting to public announcement logic equipped with a novel update procedure. - oai:arXiv.org:2511.02942v1 - math.LO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Ekaterina Kubyshkina, Marcio Kl\'eos Pereira, Mattia Petrolo - - - Well-posedness for 2D non-homogeneous incompressible fluids with general density-dependent odd viscosity - https://arxiv.org/abs/2511.02948 - arXiv:2511.02948v1 Announce Type: new -Abstract: We study the initial value problem for a system of equations describing the motion of two-dimensional non-homogeneous incompressible fluids exhibiting odd (non-dissipative) viscosity effects. We consider the complete odd viscous stress tensor with a general density-dependent viscosity coefficient $f(\rho)$. Under suitable assumptions, we prove the local existence and uniqueness of strong solutions in $H^s(\mathbb{R}^2)$ $(s>2)$, for a class of viscosity coefficients covering the particular case $f(\rho)=a\rho^\alpha+b$ for any $(a,b,\alpha)\in\mathbb{R}^3$, generalising the result of Fanelli, Granero-Belinch\'on and Scrobogna, devoted to the case $f(\rho)=\rho$. Additionally, we are able to do so without requiring the initial density variation to belong to $L^2(\mathbb{R}^2)$. As a major step of the proof, we exhibit an effective velocity for this sytem, generalising the so-called "Els\"asser formulation" recently derived by Fanelli and Vasseur. - oai:arXiv.org:2511.02948v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Matthieu Pageard - - - List Decoding and New Bicycle Code Constructions for Quantum LDPC Codes - https://arxiv.org/abs/2511.02951 - arXiv:2511.02951v1 Announce Type: new -Abstract: In this paper, we propose a new decoder, called the Multiple-Bases Belief-Propagation List Decoder (MBBP-LD), for Quantum Low-Density Parity-Check (QLDPC) codes. It extends the Multiple-Bases Belief-Propagation (MBBP) framework, originally developed for classical cyclic LDPC codes. The proposed method preserves the linear-time complexity of standard BP decoder while improving the logical error rate. To further reduce the logical error rate, a new decision rule is introduced for the post-processing list decoder, outperforming the conventional least-metric selector (LMS) criterion. For the recently developed and implemented bivariate bicycle (BB) code with parameters \([[144,12,12]]\), our proposed MBBP-LD decoder achieves up to 40\% lower logical error rate compared to the state-of-the-art decoder for short QLDPC codes, i.e., BP with ordered-statistics decoding (BP-OSD), while retaining the linear-time complexity of the plain BP decoder. In addition, we explore a new subclass of BB codes, that we refer to as the univariate bicycle (UB) codes, specifically with lower-weight parity checks (\(w=6,8\)). This reduces the polynomial search space for the code compared to general BB codes, i.e., by reducing the search space over two polynomial components in BB codes to just a single polynomial component in UB codes. Simulations demonstrate the promising performance of these codes under various types of BP decoders. - oai:arXiv.org:2511.02951v1 - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Sheida Rabeti, Hessam Mahdavifar - - - Necessary and Sufficient Conditions for Characterizing Finite Discrete Distributions with Generalized Shannon's Entropy - https://arxiv.org/abs/2511.02955 - arXiv:2511.02955v1 Announce Type: new -Abstract: This article establishes necessary and sufficient conditions under which a finite set of Generalized Shannon's Entropy (GSE) characterizes a finite discrete distribution up to permutation. For an alphabet of cardinality K, it is shown that K-1 distinct positive real orders of GSE are sufficient (and necessary if no multiplicity) to identify the distribution up to permutation. When the distribution has a known multiplicity structure with s distinct values, s-1 orders are sufficient and necessary. These results provide a label-invariant foundation for inference on unordered sample spaces and enable practical goodness-of-fit procedures across disparate alphabets. The findings also suggest new approaches for testing, estimation, and model comparison in settings where moment-based and link-based methods are inadequate. - oai:arXiv.org:2511.02955v1 - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Jialin Zhang - - - Graphs with asymmetric Ramsey properties - https://arxiv.org/abs/2511.02963 - arXiv:2511.02963v1 Announce Type: new -Abstract: Given positive integers $k$ and $\ell$ we write $G \rightarrow (K_k,K_\ell)$ if every 2-colouring of the edges of $G$ yields a red copy of $K_k$ or a blue copy of $K_\ell$ and we denote by $R(k)$ the minimum $n$ such that $K_n\rightarrow (K_k,K_k)$. By using probabilistic methods and hypergraph containers we prove that for every integer $k \geq 3$, there exists a graph $G$ such that $G \nrightarrow (K_k,K_k)$ and $G \rightarrow (K_{R(k)-1},K_{k-1})$. This result can be viewed as a variation of a classical theorem of Ne\v{s}et\v{r}il and R\"odl [The Ramsey property for graphs with forbidden complete subgraphs, Journal of Combinatorial Theory, Series B, 20 (1976), 243-249], who proved that for every integer $k\geq 2$ there exists a graph $G$ with no copies of $K_k$ such that $G\rightarrow(K_{k-1}, K_{k-1})$. - oai:arXiv.org:2511.02963v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Walner Mendon\c{c}a, Meysam Miralaei, Guilherme O. Mota - - - Lemma on logarithmic derivative over directed manifolds - https://arxiv.org/abs/2511.02972 - arXiv:2511.02972v1 Announce Type: new -Abstract: In this paper, we generalize Ahlfors' lemma on logarithmic derivative to holomorphic tangent curves of directed projective manifolds intersecting closed subschemes. As a consequence, we obtain Algebro-Geometric Ahlfors' Lemma on Logarithmic Derivative (AALD for short) and General form of Algebro-Geometric Version of Ahlfors' Lemma on Logarithmic Derivative (GAALD for short) for holomorphic tangent curves of directed projective manifolds. We also get a transform of AALD and GAALD with respect to a linear system. Finally, we get the Second Main Theorem type results for holomorphic curves as the applications of GAALD and its transform. - oai:arXiv.org:2511.02972v1 - math.CV - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Peiqiang Lin - - - Sections and projections of the outer and inner regularizations of a convex body - https://arxiv.org/abs/2511.02974 - arXiv:2511.02974v1 Announce Type: new -Abstract: We establish new geometric inequalities comparing the volumes of sections and projections of a convex body, whose barycenter or Santal\'o point is at the origin, with those of its inner and outer regularizations. We also provide functional extensions of these inequalities to the setting of log-concave functions. Our approach relies on the recent optimal $M$-estimate of Bizeul and Klartag for isotropic convex bodies. - oai:arXiv.org:2511.02974v1 - math.MG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Natalia Tziotziou - - - Spectral analysis, maximum principles and shape optimization for nonlinear superposition operators of mixed fractional order - https://arxiv.org/abs/2511.02978 - arXiv:2511.02978v1 Announce Type: new -Abstract: The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition operators" defined as continuous superpositions of operators of mixed fractional order, modulated by a signed finite Borel measure on the unit interval. This framework encompasses, as particular cases, mixed local and nonlocal operators such as $-\Delta_p+(-\Delta_p)^s$, finite (possibly infinite) sums of fractional $p$-Laplacians with different orders, as well as operators involving fractional Laplacians with ``wrong" signs. - The main findings, obtained through variational techniques, concern the spectral analysis of the Dirichlet eigenvalue problem associated with general superposition operators with special emphasis on various properties of the first eigenvalue and its corresponding eigenfunction. - We establish weak and strong maximum principles for positive superposition operators by introducing an appropriate notion of the {\it nonlocal tail} for this class of superposition operators and deriving a logarithmic estimate, both of which are of independent interest. Utilizing these newly developed tools, we further investigate the spectral properties of such superposition operators and prove that the first eigenvalue is isolated. Moreover, we show that the eigenfunctions corresponding to positive eigenvalues are globally bounded and that they change sign when associated with higher eigenvalues. In addition, we demonstrate that the second eigenvalue is well-defined and provide the mountain pass characterization. - Finally, we address shape optimization problems, in particular, the Faber--Krahn inequality associated with the principal frequency associated with the superposition operators. - oai:arXiv.org:2511.02978v1 - math.AP - math.SP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar, Michael Ruzhansky - - - The Formal Context of Saturated Transfer Systems on Finite Abelian Groups - https://arxiv.org/abs/2511.02982 - arXiv:2511.02982v1 Announce Type: new -Abstract: We describe the reduced formal context of the lattice of saturated transfer systems on a finite abelian group. As an application, we compute that there are 13,784,538,270,571 saturated transfer systems on the elementary abelian group $C_5^3$. - oai:arXiv.org:2511.02982v1 - math.CO - math.AT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Seth Bernstein, Ben Spitz - - - Towards a geometric characterization of unbounded integer cubic optimization problems via thin rays - https://arxiv.org/abs/2511.02983 - arXiv:2511.02983v1 Announce Type: new -Abstract: We study geometric characterizations of unbounded integer polynomial optimization problems. While unboundedness along a ray fully characterizes unbounded integer linear and quadratic optimization problems, we show that this is not the case for cubic polynomials. To overcome this, we introduce thin rays, which are rays with an arbitrarily small neighborhood, and prove that they characterize unboundedness for integer cubic optimization problems in dimension up to three, and we conjecture that the same holds in all dimensions. Our techniques also provide a complete characterization of unbounded integer quadratic optimization problems in arbitrary dimension, without assuming rational coefficients. These results underscore the significance of thin rays and offer new tools for analyzing integer polynomial optimization problems beyond the quadratic case. - oai:arXiv.org:2511.02983v1 - math.OC - cs.DM - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alberto Del Pia - - - A classification of unitals in nearfield planes with maximal automorphism group - https://arxiv.org/abs/2511.02987 - arXiv:2511.02987v1 Announce Type: new -Abstract: We classify the parabolic unitals in regular nearfield planes of odd order $q^2$ whose linear collineation group has the maximal size of $q^3-q$. We also establish a number of more general results concerning parabolic unitals in regular nearfield planes under weaker assumptions. - oai:arXiv.org:2511.02987v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Randon J. Weaver, Robert S. Coulter, Alice M. W. Hui - - - Projection-width: a unifying structural parameter for separable discrete optimization - https://arxiv.org/abs/2511.02990 - arXiv:2511.02990v1 Announce Type: new -Abstract: We introduce the notion of projection-width for systems of separable constraints, defined via branch decompositions of variables and constraints. We show that several fundamental discrete optimization and counting problems can be solved in polynomial time when the projection-width is polynomially bounded. These include optimization, counting, top-k, and weighted constraint violation. Our results identify a broad class of tractable nonlinear discrete optimization and counting problems. Even when restricted to the linear setting, they subsume and substantially extend some of the strongest known tractability results across multiple research areas: integer linear optimization, binary polynomial optimization, and Boolean satisfiability. Although these results originated independently within different communities and for seemingly distinct problem classes, our framework unifies and significantly generalizes them under a single structural perspective. - oai:arXiv.org:2511.02990v1 - math.OC - cs.DM - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alberto Del Pia - - - Commuting graphs and semigroup constructions - https://arxiv.org/abs/2511.03003 - arXiv:2511.03003v1 Announce Type: new -Abstract: The aim of this paper is to see how commuting graphs interact with two semigroup constructions: the zero-union and the direct product. For both semigroup constructions, we investigate the diameter, clique number, girth, chromatic number and knit degree of their commuting graphs and, when possible, we exhibit the relationship between each one of these properties and the corresponding properties of the commuting graphs of the original semigroups. - oai:arXiv.org:2511.03003v1 - math.CO - math.GR - math.RA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - T\^ania Paulista - - - Triangular gaps in the most frequent sizes of $hA$ for $|A|=4$ - https://arxiv.org/abs/2511.03008 - arXiv:2511.03008v1 Announce Type: new -Abstract: We explain the triangular gaps observed experimentally in the most popular sizes of the $h$-fold iterated sumset, $hA,$ when $A$ is a randomly chosen four-element subset of the first $q$ natural numbers, for $q$ much larger than $h.$ - oai:arXiv.org:2511.03008v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Steven Senger - - - The Bailey-Zeta Transform and its Classical Limit to the Riemann Zeta Function - https://arxiv.org/abs/2511.03009 - arXiv:2511.03009v1 Announce Type: new -Abstract: We develop a unified analytic and algebraic framework connecting the theory of Bailey pairs with $q$-deformations of the Riemann zeta function. First, an algebraic theorem (Bailey-Zeta transform) extends the classical Bailey lemma to sequences weighted by a zeta-type factor $q^{sr}$. Next, we establish rigorously that the generating function arising from the pair $\alpha_r\equiv1$ converges, under the scaling $(1-q)^s$, to $\zeta(s)$ as $q\to1^-$. A $q$-analogue of the Euler--Mascheroni constant naturally emerges from this framework, and its limit is shown to recover $\gamma$. The approach highlights a deep correspondence between combinatorial $q$-series identities and analytic number theory. - oai:arXiv.org:2511.03009v1 - math.GM - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Mahipal Gurram - - - AdditiveToricVarieties: A Macaulay2 package for working with additive complete toric varieties - https://arxiv.org/abs/2511.03024 - arXiv:2511.03024v1 Announce Type: new -Abstract: We introduce the AdditiveToricVarieties package for Macaulay2, a software system for algebraic geometry and commutative algebra, with methods for working with additive group actions on complete toric varieties. More precisely, we implement algorithms, based on results by Arzhantsev, Dzhunusov and Romaskevich, to determine whether a complete toric variety admits an action of the commutative unipotent group and whether it is unique or not. We also observe that every smooth complete toric variety of Picard rank two is additive. We apply our methods to the class of smooth Fano toric varieties and notably determine all such varieties of dimension up to 6 admitting an additive action. - oai:arXiv.org:2511.03024v1 - math.AG - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Fabi\'an Levic\'an, Pedro Montero - - - Chromatic numbers of rank-two Abelian Cayley graphs - https://arxiv.org/abs/2511.03028 - arXiv:2511.03028v1 Announce Type: new -Abstract: A connected Cayley graph for an Abelian group generated by a finite symmetric subset $S$ can be represented by an integer matrix, its Heuberger matrix. We call the number of columns of that matrix its rank and the number of rows its dimension. Several previous papers have dealt with the question of finding a formula for the chromatic number of an Abelian Cayley graph in terms of an associated Heuberger matrix. In this paper, we fully resolve this matter for all integer matrices of rank $\leq 2$. Prior results provide such formulas when the rank is 1, as well as when the rank is 2 and the dimension is no more than 4. Here, we complete the picture for the rank-two case by showing that when the rank is 2 and the dimension is at least 5, then the chromatic number equals 3 unless the graph has loops (in which case it is uncolorable); the graph is bipartite (in which case the chromatic number is 2); or the matrix has a zero row (in which case, the chromatic number does not change when that row is deleted). - oai:arXiv.org:2511.03028v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Mike Krebs, Alejandro Leyva - - - Carl St{\o}rmer and his Numbers - https://arxiv.org/abs/2511.03030 - arXiv:2511.03030v1 Announce Type: new -Abstract: In many proofs of Fermat's Two Squares Theorem, the smallest least residue solution $x_0$ of the quadratic congruence $x^2 \equiv -1 \bmod p$ plays an essential role; here $p$ is prime and $p \equiv 1 \bmod 4$. Such an $x_0$ is called a St{\o}rmer number, named after the Norwegian mathematician and astronomer Carl St{\o}rmer (1874-1957). In this paper, we establish necessary and sufficient conditions for $x_0 \in \mathbb{N}$ to be a St{\o}rmer number of some prime $p \equiv 1 \bmod 4$. St{\o}rmer's main interest in his investigations of St{\o}rmer numbers stemmed from his study of identities expressing $\pi$ as finite linear combinations of certain values of the Gregory-MacLaurin series for $\arctan(1/x)$. Since less than 600 digits of $\pi$ were known by 1900, approximating $\pi$ was an important topic. One such identity, discovered by St{\o}rmer in 1896, was used by Yasumasa Kanada and his team in 2002 to obtain 1.24 trillion digits of $\pi$. We also discuss St{\o}rmer's work on connecting these numbers to Gregory numbers and approximations of $\pi$. \u - oai:arXiv.org:2511.03030v1 - math.HO - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Matthew Kroesche, Lance L. Littlejohn, Graeme Reinhart - - - Robust optimal consumption, investment and reinsurance for recursive preferences - https://arxiv.org/abs/2511.03031 - arXiv:2511.03031v1 Announce Type: new -Abstract: This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer's surplus follows the diffusion approximation of the Cram\'er-Lundberg model, and the insurer can purchase proportional reinsurance. Model ambiguity is characterised by a class of equivalent probability measures, and the insurer, being ambiguity-averse, aims to maximise utility under the worst-case scenario. By solving the associated coupled forward-backward stochastic differential equation (FBSDE), we derive closed-form solutions for the optimal strategies and the value function. Our analysis reveals how ambiguity aversion, risk aversion, and the elasticity of intertemporal substitution (EIS) influence the optimal policies. Numerical experiments illustrate the effects of key parameters, showing that optimal consumption decreases with higher risk aversion and EIS, while investment and reinsurance strategies are co-dependent on both financial and insurance market parameters, even without correlation. This study provides a comprehensive framework for insurers to manage capital allocation and risk transfer under deep uncertainty. - oai:arXiv.org:2511.03031v1 - math.OC - q-fin.RM - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Elizabeth Dadzie, Wilfried Kuissi-Kamdem, Marcel Ndengo - - - On Hydrodynamic Implosions and the Landau-Coulomb Equation - https://arxiv.org/abs/2511.03033 - arXiv:2511.03033v1 Announce Type: new -Abstract: We study the inhomogeneous Landau equation with Coulomb potential and derive a new continuation criterion: a smooth solution can be uniquely continued for as long as it remains bounded. This provides, to our knowledge, the first continuation criterion based on a quantity not controlling the mass density. Consequently, we are able to rule out a potential singularity formation scenario known as tail fattening, in which an implosion occurs due to the loss of decay at large velocities. - More generally, we are able to rule out almost all Type II approximately self-similar blow-up rates, without any assumption of decay on the inner profile, complementing existing Type I blow-up analysis in the literature. Heuristically, this suggests that it should be impossible to directly use the hydrodynamic limit connection with the 3D compressible Euler equations to construct a singular solution to the Landau equation with Coulomb potential. Such a potential implosion scenario -- based on either an isentropic or non-isentropic implosion for the 3D Euler equations -- would naturally result in a Type II approximately self-similar blow-up scenario, falling well within the range our theorem. - oai:arXiv.org:2511.03033v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - William Golding, Christopher Henderson - - - A labeling of the Simplex-Lattice Hypergraph with at most 2 colors on each hyperedge - https://arxiv.org/abs/2511.03036 - arXiv:2511.03036v1 Announce Type: new -Abstract: This paper provides a positive answer to the question of Mirzakhani and Vondrak that asks if there is a Sperner-admissible labeling of the simplex-lattice hypergraph such that each hyperedge uses at most 2 colors. - oai:arXiv.org:2511.03036v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Ognjen Papaz, Du\v{s}ko Joji\'c - - - Last Hitting Time Distributions for Solvable Diffusions - https://arxiv.org/abs/2511.03037 - arXiv:2511.03037v1 Announce Type: new -Abstract: By considering any one-dimensional time-homogeneous solvable diffusion process,this paper develops a complete analytical framework for computing the distribution of the last hitting time, to any level, and its joint distribution with the process value on any finite time horizon. Our formalism allows for regular diffusions with any type of endpoint boundaries. We exploit the inherent link between last and first hitting times. The simpler known formula for the marginal distribution of the last hitting time on an infinite time horizon is easily recovered as a special limit. Furthermore, we derive general formulae for each component of the joint distribution, i.e., the jointly continuous, the partly continuous (defective) and the jointly defective portions. By employing spectral expansions of the transition densities and the first hitting time distributions, our derivations culminate in novel general spectral expansions for both marginal and joint distributions of the last hitting time and the process value on any finite time horizon. - An additional main contribution of this paper lies in the application of our general formulae, giving rise to newly closed-form analytical formulae for several solvable diffusions. In particular, we systematically derive analytical expressions for each portion of the marginal and joint distributions of the last hitting time and the process value on any finite time horizon, without and with imposed killing at one or two interior points, for Brownian motion, Brownian motion with drift (geometric Brownian motion), the squared Bessel , squared radial Ornstein-Uhlenbeck (CIR) and Ornstein-Uhlenbeck processes. Most of our formulae are given in terms of spectral series that are rapidly convergent and efficiently implemented. We demonstrate this by presenting some numerical calculations of marginal and joint distributions using accurately truncated series. - oai:arXiv.org:2511.03037v1 - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Giuseppe Campolieti, Yaode Sui - - - A partial order on the 240 packings of PG(3,2) - https://arxiv.org/abs/2511.03040 - arXiv:2511.03040v1 Announce Type: new -Abstract: It has long been known that the most symmetrical solutions of Kirkman's Schoolgirl Problem can be constructed from the $240$ packings of the projective space $PG(3, 2)$, but it seems to have escaped notice that these packings have the structure of a partially ordered set. In this paper, we construct a shellable Bruhat-like graded partial order on the packings of $PG(3, 2)$ that refines the partial order on the product of four chains $[8]\times[5]\times[3]\times[2]$ and defines a Lehmer code on the packings. The partial order exists because the packings of $PG(3, 2)$ form a quasiparabolic set (in the sense of Rains--Vazirani) that is in bijective correspondence with a certain collection of maximal orthogonal subsets of the $E_8$ root system. The $E_8$ construction also induces transitive actions of the Weyl groups of type $D_n$ on the packings for $5 \leq n \leq 8$, and these actions are faithful for $n < 8$. It is possible to define both the signed permutation action and the partial order using the combinatorics of labelled Fano planes. - oai:arXiv.org:2511.03040v1 - math.CO - math.GR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - R. M. Green - - - Partial Cohomologically Complete Intersections via Hodge Theory - https://arxiv.org/abs/2511.03042 - arXiv:2511.03042v1 Announce Type: new -Abstract: Using Saito's theory of mixed Hodge modules, we study a generalization of Hellus-Schenzel's "cohomologically complete intersection" property. This property is equivalent to perversity of the shifted constant sheaf. We relate the generalized version to the Hodge filtration on local cohomology, depth of Du Bois complexes, Hodge-Lyubeznik numbers and prove a striking inequality on the codimension of the non-perverse locus of the shifted constant sheaf. - We study the case of cones over projective rational homology manifolds. We study when such varieties satisfy the weakened condition mentioned above as well as the partial Poincar\'{e} duality. To do this, we completely describe their higher local cohomology modules in terms of the Hodge theory of the corresponding projective variety. We apply this to the study of Hodge-Lyubeznik numbers and the intersection cohomology. - oai:arXiv.org:2511.03042v1 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Qianyu Chen, Bradley Dirks, Sebastian Olano - - - Min-Max Optimization Is Strictly Easier Than Variational Inequalities - https://arxiv.org/abs/2511.03052 - arXiv:2511.03052v1 Announce Type: new -Abstract: Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by bypassing this reduction? This paper initiates this investigation. We show that the answer is yes in the textbook setting of unconstrained quadratic objectives: the optimal convergence rate for first-order algorithms is strictly better for min-max problems than for the corresponding variational inequalities. The key reason that min-max algorithms can be faster is that they can exploit the asymmetry of the min and max variables--a property that is lost in the reduction to variational inequalities. Central to our analyses are sharp characterizations of optimal convergence rates in terms of extremal polynomials which we compute using Green's functions and conformal mappings. - oai:arXiv.org:2511.03052v1 - math.OC - cs.DS - cs.LG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Henry Shugart, Jason M. Altschuler - - - Read Between the Hyperplanes: On Spectral Projection and Sampling Approaches to Randomized Kaczmarz - https://arxiv.org/abs/2511.03055 - arXiv:2511.03055v1 Announce Type: new -Abstract: Among recent developments centered around Randomized Kaczmarz (RK), a row-sampling iterative projection method for large-scale linear systems, several adaptions to the method have inspired faster convergence. Focusing solely on ill-conditioned and overdetermined linear systems, we highlight inter-row relationships that can be leveraged to guide directionally aware projections. In particular, we find that improved convergence rates can be made by (i) projecting onto pairwise row differences, (ii) sampling from partitioned clusters of nearly orthogonal rows, or (iii) more frequently sampling spectrally-diverse rows. - oai:arXiv.org:2511.03055v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - James Nguyen, Oleg Presnyakov, Aditya Radhakhrishnan - - - A novel linear transport model with distinct scattering mechanisms for direction and speed - https://arxiv.org/abs/2511.03058 - arXiv:2511.03058v1 Announce Type: new -Abstract: We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These scattering processes occur at different time scales and with different intensities, leading to a kinetic equation where the total scattering operator is the sum of two separate operators. Each of them depends not only on the kernel characterizing the corresponding scattering mechanism, but also explicitly on the marginal distribution of either the speed or the direction. Therefore, unlike classical settings, the gain terms in our operators are not tied to a fixed equilibrium distribution but evolve in time through the marginals. As a result, typical analytical tools from kinetic theory, such as equilibrium characterization, entropy methods, spectral analysis in Hilbert spaces, and Fredholm theory, are not applicable in a standard fashion. In this work, we rigorously analyze the properties of this new class of scattering operators, including the structure of their non-standard pseudo-inverses and their asymptotic behavior. We also derive macroscopic (hydrodynamic) limits under different regimes of scattering frequencies, revealing new effective equations and highlighting the interplay between speed and directional relaxation. - oai:arXiv.org:2511.03058v1 - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Martina Conte, Nadia Loy - - - New Numeric Invariants of an Unfolding of a Polycycle "Tears of the Heart" - https://arxiv.org/abs/2511.03062 - arXiv:2511.03062v1 Announce Type: new -Abstract: In this paper new numeric invariants of structurally unstable vector fields in the plane are found. One of the main tools is an improved asymptotics of sparkling saddle connections that occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological invariant of two arithmetic progressions, both perturbed and unperturbed, on the real line. For the pairs of the unperturbed arithmetic progressions we give a complete topological classification. - oai:arXiv.org:2511.03062v1 - math.DS - math.CA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yulij Ilyashenko, Stanislav Minkov, Ivan Shilin - - - A Tsallis-Entropy Lens on Genetic Variation - https://arxiv.org/abs/2511.03063 - arXiv:2511.03063v1 Announce Type: new -Abstract: We introduce an information-theoretic generalization of the fixation statistic, the Tsallis-order $q$ F-statistic, $F_q$, which measures the fraction of Tsallis $q$-entropy lost within subpopulations relative to the pooled population. The family nests the classical variance-based fixation index $F_{\textbf{ST}}$ at $q{=}2$ and a Shannon-entropy analogue at $q{=}1$, whose absolute form equals the mutual information between alleles and population labels. By varying $q$, $F_q$ acts as a spectral differentiator that up-weights rare variants at low $q$, while $q{>}1$ increasingly emphasizes common variants, providing a more fine-grained view of differentiation than $F_{\textbf{ST}}$ when allele-frequency spectra are skewed. On real data (865 Oceanian genomes with 1,823,000 sites) and controlled genealogical simulations (seeded from 1,432 founders from HGDP and 1000 Genomes panels, with 322,216 sites), we show that $F_q$ in One-vs-Rest (OVR) and Leave-One-Out (LOO) modes provides clear attribution of which subpopulations drive regional structure, and sensitively timestamps isolation-migration events and founder effects. $F_q$ serves as finer-resolution complement for simulation audits and population-structure summaries. - oai:arXiv.org:2511.03063v1 - cs.IT - cs.CE - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Margarita Geleta, Daniel Mas Montserrat, Alexander G. Ioannidis - - - Polynomials Arising from Sorted Binomial Coefficients - https://arxiv.org/abs/2511.03082 - arXiv:2511.03082v1 Announce Type: new -Abstract: The triangle of sorted binomial coefficients $\left\langle {n \atop k} \right\rangle = \binom{n}{\lfloor \frac{n - k}{2} \rfloor}$ for $0 \leq k \leq n$ has appeared several times in recent combinatorial works but has evaded dedicated study. Here we refer to $\left\langle {n \atop k} \right\rangle$ as the Pascalian numbers and unify the various perspectives of $\left\langle {n \atop k} \right\rangle$. We then view each row of the $\left\langle {n \atop k} \right\rangle$ triangle as the coefficients of the $n$th Pascalian polynomial, which we denote $P_n(z)$. We derive recursions, formulae, and bounds on $P_n(z)$'s roots in $\mathbb{C}$, and characterize the asymptotics of these roots. We show the roots of $P_n(z)$ converge uniformly to a curve $\partial \Gamma \subset \mathbb{C}$ and asymptotically fill the curve densely. We conclude with a discussion of the reducibility and Galois groups of $P_n(z)$. Our work has natural connections to the truncated binomial polynomials, asymptotic analysis, and well-known integer families. - oai:arXiv.org:2511.03082v1 - math.CO - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Owen John Levens - - - Cycle lengths in graphs of given minimum degree - https://arxiv.org/abs/2511.03085 - arXiv:2511.03085v1 Announce Type: new -Abstract: In a graph, $k$ cycles are {\em admissible} if their lengths form an arithmetic progression with common difference one or two. Let $G$ be a 2-connected graph with minimum degree at least $k\geqslant 4$. We prove that - \begin{itemize} - \item [(1)] $G$ contains $k$ admissible cycles, unless $G\cong K_{k+1}$ or $K_{k,n-k}$; - \item [(2)] $G$ contains cycles of lengths $\ell$ modulo $k$ for all even $\ell$, unless $G\cong K_{k+1}$ or $K_{k,n-k}$; - \item [(3)] $G$ contains cycles of lengths $\ell$ modulo $k$ for all $\ell$, unless $G\cong K_{k+1}$ or $G$ is bipartite. - \end{itemize} In addition, we show that if $k$ is even and $G$ is 2-connected with minimum degree at least $k-1$ and order at least $k+2$, then $G$ contains cycles of lengths $\ell$ modulo $k$ for all even $\ell$. These findings provide a stability analysis of the main results on cycle lengths in graphs of given minimum degree in [J. Gao, Q. Huo, C. Liu, J. Ma, A unified proof of conjectures on cycle lengths in graphs, International Mathematics Research Notices 2022 (10) (2022) 7615--7653]. As a corollary, we determine the maximum number of edges in a graph that does not contain a cycle of length 0 modulo $k$ for all odd $k$. - oai:arXiv.org:2511.03085v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Yandong Bai, Andrzej Grzesik, Binlong Li, Magdalena Prorok - - - Coxeter groups and the proper joint spectrums of their faithful representations - https://arxiv.org/abs/2511.03101 - arXiv:2511.03101v1 Announce Type: new -Abstract: In this paper, we analyze the faithful representations of the dihedral groups, and prove that the Coxeter groups can be determined by the proper joint spectrum of their faithful representations. - oai:arXiv.org:2511.03101v1 - math.RT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Shoumin Liu, Zhaohuan Peng, Xumin Wang - - - Parametric Hierarchical Matrix Approximations to Kernel Matrices - https://arxiv.org/abs/2511.03109 - arXiv:2511.03109v1 Announce Type: new -Abstract: Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a class of matrices known as hierarchical matrices. A hierarchical matrix consists of a hierarchy of small near-field blocks (or sub-matrices) stored in a dense format and large far-field blocks approximated by low-rank matrices. Standard methods for forming hierarchical matrices do not account for the fact that kernel matrices depend on specific hyperparameters; for example, in the context of Gaussian processes, hyperparameters must be optimized over a fixed parameter space. We introduce a new class of hierarchical matrices, namely, parametric (parameter-dependent) hierarchical matrices. Members of this new class are parametric $\mathcal{H}$-matrices and parametric $\mathcal{H}^{2}$-matrices. The construction of a parametric hierarchical matrix follows an offline-online paradigm. In the offline stage, the near-field and far-field blocks are approximated by using polynomial approximation and tensor compression. In the online stage, for a particular hyperparameter, the parametric hierarchical matrix is instantiated efficiently as a standard hierarchical matrix. The asymptotic costs for storage and computation in the offline stage are comparable to the corresponding standard approaches of forming a hierarchical matrix. However, the online stage of our approach requires no new kernel evaluations, and the far-field blocks can be computed more efficiently than standard approaches. {Numerical experiments show over $100\times$ speedups compared with existing techniques.} - oai:arXiv.org:2511.03109v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Abraham Khan, Chao Chen, Vishwas Rao, Arvind K. Saibaba - - - Efficient linear schemes for a penalized ternary Cahn-Hilliard system - https://arxiv.org/abs/2511.03111 - arXiv:2511.03111v1 Announce Type: new -Abstract: In this work we introduce novel numerical schemes for a penalized version of the ternary Cahn-Hilliard system for the purpose of creating accurate and efficient numerical schemes of interfacial dynamics with three components as well as some results extending these ideas to systems with four or more components. The first scheme is linear, decoupled, first order accurate, and unconditionally energy stable. Next, we present a second scheme which is a conditionally energy stable modification of the first scheme, but has greatly reduced computational cost. Finally, we present a third scheme which is linear and second order accurate but the unknowns are coupled. Moreover, we present several numerical simulations in two and three dimensions to give a comprehensive overview of each scheme and the cost-benefit analysis associated with designing a method for energy-stability, efficiency, and accuracy. - oai:arXiv.org:2511.03111v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Justin Swain, Giordano Tierra - - - Optimal Boundary Control of Diffusion on Graphs via Linear Programming - https://arxiv.org/abs/2511.03129 - arXiv:2511.03129v1 Announce Type: new -Abstract: We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by edge lengths to preserve geometric fidelity. Boundary potentials act as controls that drive interior fluxes according to a linear network Laplacian. The optimization problem enforces physically meaningful sign and flux-cap constraints at all boundary edges, derived directly from a gradient bound. This yields a finite-dimensional LP whose feasible set is polyhedral, and whose boundedness and solvability follow from simple geometric or algebraic conditions on the network data. - We prove that under the absence of negative recession directions--automatically satisfied in the presence of finite box bounds, flux caps, or sign restrictions--the LP admits a global minimizer. Several sufficient conditions guaranteeing boundedness of the feasible region are identified, covering both full-rank and rank-deficient flux maps. The analysis connects classical results such as the Minkowski--Weyl decomposition, Hoffman's bound, and the fundamental theorem of linear programming with modern network-based diffusion modeling. - Two large-scale examples illustrate the framework: (i) A typical large stadium in a major modern city, which forms a single connected component with relatively uniform corridor widths, and a (ii) A complex street network emanating from a large, historical city center, which forms a multi-component system. - oai:arXiv.org:2511.03129v1 - math.OC - cs.AI - physics.comp-ph - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Harbir Antil, Rainald L\"ohner, Felipe P\'erez - - - A Variational Approach to Planar Choreographies via Ekeland's Principle - https://arxiv.org/abs/2511.03134 - arXiv:2511.03134v1 Announce Type: new -Abstract: We present a variational approach to obtain periodic solutions of the $N$-body problem, in particular the 'figure-eight' solution for three equal masses. The central idea is to explicitly optimize the \emph{spatial scale} within the Lagrangian action, leading to the functional $\mathcal F = K^{\alpha/(\alpha+2)} V^{2/(\alpha+2)}$. We prove the existence of critical points of $\mathcal F$ that enforce a curve with a single self-crossing, and show that every reparametrized critical curve satisfies Newton's equations and is free of collisions. This framework recovers the Chenciner-Montgomery 'eight' (for $\alpha=1$) and extends to the whole range $0<\alpha<2$. - oai:arXiv.org:2511.03134v1 - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Juan Manuel S\'anchez-Cerritos, Mayte Torres-Hern\'andez - - - A common generalization to strengthenings of Drisko's Theorem for intersections of two matroids - https://arxiv.org/abs/2511.03135 - arXiv:2511.03135v1 Announce Type: new -Abstract: Let $\mathcal{M}$ and $\mathcal{N}$ be two matroids on the same ground set $V$. Let $A_1,\dots,A_{2n-1}$ be sets which are independent in both $\mathcal{M}$ and $\mathcal{N}$, satisfying $|A_i|\geq \textrm{min}(i,n)$ for all $i$. We show that there exists a partial rainbow set of size $n$, which is independent in both $\mathcal{M}$ and $\mathcal{N}$. This is a common generalization of rainbow matching results for bipartite graphs by Aharoni, Berger, Kotlar, and Ziv, and for the intersection of two matroid by Kotlar and Ziv. - oai:arXiv.org:2511.03135v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Eli Berger, Daniel McGinnis - - - The isogeometric boundary element algorithm for solving the plane strain problem of an elastic matrix containing an open material surface of arbitrary shape - https://arxiv.org/abs/2511.03141 - arXiv:2511.03141v1 Announce Type: new -Abstract: The paper presents the Isogeometric Boundary Element Method (IGABEM) algorithm for solving the plane strain problem of an isotropic linearly elastic matrix containing an open material surface of arbitrary shape. Theoretical developments are based on the use of the Gurtin-Murdoch model of material surfaces. The governing equations and the boundary conditions for the problem are reviewed, and analytical integral representations for the elastic fields everywhere in the material system are presented in terms of unknown traction jumps across the surface. To find the jumps, the problem is reduced to a system of singular boundary integral equations in terms of two unknown scalar components of the surface stress tensor. The system is solved numerically using the developed IGABEM algorithm in which NURBS are used to approximate the unknowns. The main steps of the algorithm are discussed and convergence studies are performed. The algorithm is validated using two benchmark problems involving the matrix subjected to a uniform far-field load and containing a surface along (i) a straight segment and (ii) a circular arc. Numerical examples are presented to illustrate the influence of governing parameters with a focus on the influence of curvature variation. - oai:arXiv.org:2511.03141v1 - math.NA - cs.NA - physics.comp-ph - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Rohit Satish Patil, Zhilin Han, Sofia G. Mogilevskaya - - - Note on the Rate of Vortex Stretching for Axisymmetric Euler Flows Without Swirl - https://arxiv.org/abs/2511.03171 - arXiv:2511.03171v1 Announce Type: new -Abstract: In this paper, we investigate Childress's conjecture proposed in [Phys.D 237(14-17):1921-1925, 2008] on the growth rate of the vorticity maximum for axisymmetric swirl-free Euler flows in three and higher dimensions. We consider the setting that the axial vorticity is non-positive in the upper half space and odd in the last coordinate, which corresponds to the flow setup for head-on collision of anti-parallel vortex rings. By introducing the \emph{generalized vertical moment} and proving its monotonicity, we obtain a lower bound for the growth of the vorticity maximum, contingent on the initial decay rate in the $z$-direction. Specifically, for three-dimensional flows with initial vorticity sufficiently fast decay in $z$, we obtain a lower bound of $t^{\frac{1}{2}-}$, thereby improving upon existing results. - oai:arXiv.org:2511.03171v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Daomin Cao, Junhong Fan, Guolin Qin - - - A Lie algebra associated with adjoint multiple zeta values - https://arxiv.org/abs/2511.03177 - arXiv:2511.03177v1 Announce Type: new -Abstract: Jarossay introduced adjoint multiple zeta values, and he found $\mathbb{Q}$-algebraic relations among adjoint multiple zeta values, referred to as the \emph{adjoint double shuffle relations}, by using Racinet's dual formulation of the generating series of multiple zeta values. Jarossay defined the affine scheme $\mathrm{AdDMR}_0$ determined by the adjoint double shuffle relations and posed a question whether $\mathrm{AdDMR}_0$ is isomorphic to Racinet's double shuffle group $\mathrm{DMR}_0$. In this paper, we refine Jarossay's question by formulating what we call the adjoint conditions and by addressing its Lie algebraic side. Within this framework, we construct the Lie algebra associated with the adjoint double shuffle relations by imposing Hirose's parity results. - oai:arXiv.org:2511.03177v1 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Takumi Anzawa - - - Random Schr\"odinger operator with singular potentials - https://arxiv.org/abs/2511.03183 - arXiv:2511.03183v1 Announce Type: new -Abstract: We survey the localization theory of random Schr\"odinger operators with singular single-site distributions, focusing on two regimes: (i) H\"older-continuous laws, where quantitative Wegner estimates enable the classical multiscale analysis (MSA); and (ii) purely atomic (Bernoulli) laws, where the failure of spectral averaging is overcome via quantitative unique continuation principles (UCP). Our discussion covers both lattice and continuum settings and highlights the analytic and combinatorial mechanisms that replace regularity of the single-site measure. - oai:arXiv.org:2511.03183v1 - math.SP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Tantan Kwan - - - Analysis and Patterns of Nonlocal Klausmeier Model - https://arxiv.org/abs/2511.03188 - arXiv:2511.03188v1 Announce Type: new -Abstract: This work studies a nonlocal extension of the Klausmeier vegetation model in $\mathbb{R}^N$ $(N \ge 1)$ that incorporates both local and nonlocal diffusion. The biomass dynamics are driven by a nonlocal convolution operator, representing anomalous and faster dispersal than the standard Laplacian acting on the water component. Using semigroup theory combined with a duality argument, we establish global well-posedness and uniform boundedness of classical solutions. Numerical simulations based on the Finite Difference Method with Forward Euler integration illustrate the qualitative effects of nonlocal diffusion and kernel size on vegetation patterns. The results demonstrate that nonlocal interactions significantly influence the spatial organization of vegetation, producing richer and more coherent structures than those arising in the classical local model. - oai:arXiv.org:2511.03188v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Md Shah Alam - - - Global Existence and Asymptotic Equivalence to Barenblatt-type Solutions for the Physical Vacuum Free Boundary Problem of Damped Compressible Euler Equations in M-D - https://arxiv.org/abs/2511.03191 - arXiv:2511.03191v1 Announce Type: new -Abstract: For the physical vacuum free boundary problem of the damped compressible Euler equations in both 2D and 3D, we prove the global existence of smooth solutions and justify their time-asymptotic equivalence to the corresponding Barenblatt self-similar solutions derived from the porous media equation under Darcy's law approximation, provided the initial data are small perturbations of the Barenblatt solutions. Building on the 3D almost global existence result in [Zeng, Arch. Ration. Mech. Anal. 239, 553--597 (2021)], our key contribution lies in improving the decay rate of the time derivative of the perturbation from $-1$ (as previously established) to $-1-\varepsilon$ for a fixed constant $\varepsilon > 0$. This critical enhancement ensures time integrability and hence global existence. Together with the previous 1D result in [Luo--Zeng, Comm. Pure Appl. Math. 69, 1354--1396 (2016)], the results obtained in this paper provide a complete answer to the question raised in [Liu, T.-P.: Jpn. J. Appl. Math. 13, 25--32 (1996)]. Moreover, we also consider the problem with time-dependent damping of the form $(1+t)^{-\lambda}$ for $0 < \lambda < 1$. Notably, our framework unifies the treatment of both time-dependent ($0 < \lambda < 1$) and time-independent ($\lambda = 0$) damping cases across dimensions. We further quantify the decay rates of the density and velocity, as well as the expansion rate of the physical vacuum boundary. - oai:arXiv.org:2511.03191v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Huihui Zeng - - - Statistical Properties of Rectified Flow - https://arxiv.org/abs/2511.03193 - arXiv:2511.03193v1 Announce Type: new -Abstract: Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these methods are scant. The rectified flow can be regarded as an approximation to optimal transport, but in contrast to other transport methods that require optimization over a function space, computing the rectified flow only requires standard statistical tools such as regression or density estimation. Because of this, one can leverage standard data analysis tools for regression and density estimation to develop empirical versions of transport maps. We study some structural properties of the rectified flow, including existence, uniqueness, and regularity, as well as the related statistical properties, such as rates of convergence and central limit theorems, for some selected estimators. To do so, we analyze separately the bounded and unbounded cases as each presents unique challenges. In both cases, we are able to establish convergence at faster rates than the ones for the usual nonparametric regression and density estimation. - oai:arXiv.org:2511.03193v1 - stat.TH - cs.LG - math.ST - stat.ME - stat.ML - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Gonzalo Mena, Arun Kumar Kuchibhotla, Larry Wasserman - - - Adaptive directional decomposition methods for nonconvex constrained optimization - https://arxiv.org/abs/2511.03210 - arXiv:2511.03210v1 Announce Type: new -Abstract: In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a decomposition strategy to balance objective reduction and constraint satisfaction, together with adaptive update of stepsizes and merit parameters. Under certain conditions, the proposed adaptive directional decomposition methods attain an iteration complexity of order \(O(\epsilon^{-2})\) for finding an \(\epsilon\)-KKT point in the deterministic setting. In the stochastic setting, we further develop stochastic variants of approaches and analyze their theoretical properties by leveraging the perturbation theory. We establish the high-probability oracle complexity to find an $\epsilon$-KKT point of order \( \tilde O(\epsilon^{-4}, \epsilon^{-6}) \) (resp. \(\tilde O(\epsilon^{-3}, \epsilon^{-5}) \)) for gradient and constraint evaluations, in the absence (resp. presence) of sample-wise smoothness. To the best of our knowledge, the obtained complexity bounds are comparable to, or improve upon, the state-of-the-art results in the literature. - oai:arXiv.org:2511.03210v1 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Qiankun Shi, Xiao Wang - - - On Coefficient problems for classes $\mathcal{S}_e^{\ast}$ and $\mathcal{C}_e$ - https://arxiv.org/abs/2511.03218 - arXiv:2511.03218v1 Announce Type: new -Abstract: Logarithmic coefficients play a crucial role in the theory of univalent functions. In this study,we focus on the classes $\mathcal{S}_e^\ast$ and $\mathcal{C}_e$ of starlike and convex functions, respectively, - \begin{align*} - \mathcal{S}_e^\ast := \left\{ f \in \mathcal{S} : \frac{zf'(z)}{f(z)} \prec e^z, \ z \in \mathbb{D} \right\}, \end{align*} and \begin{align*} - \mathcal{C}_e := \left\{ f \in \mathcal{S} : 1 + \frac{z f''(z)}{f'(z)} \prec e^z, \ z \in \mathbb{D} \right\}. \end{align*} - This paper investigates the sharp bounds of the logarithmic coefficients and the Hermitian-Toeplitz determinant of these coefficients for the classes $\mathcal{S}_e^\ast$ and $\mathcal{C}_e$. Additionally, we examine the generalized Zalcman conjecture and the generalized Fekete-Szeg\"o inequality for these classes $\mathcal{S}_e^\ast$ and $\mathcal{C}_e$ and show that the inequalities are sharp. - oai:arXiv.org:2511.03218v1 - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Sujoy Majumder, Nabadwip Sarkar, Molla Basir Ahamed - - - The pretzel knot $P(4, -3, 5)$ is not squeezed - https://arxiv.org/abs/2511.03224 - arXiv:2511.03224v1 Announce Type: new -Abstract: We prove that an infinite family of three-strand pretzel knots is not squeezed. In particular, we show that $P(4, -3, 5)$ is not squeezed. This answers a question posed by Lewark (2024). Our proof is obtained by comparing the Rasmussen invariant with the $q_M$-invariant introduced by Iida and Taniguchi. - oai:arXiv.org:2511.03224v1 - math.GT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nobuo Iida, Tatsumasa Suzuki - - - The structure of $\Delta(1, 2, 2)$-free tournaments - https://arxiv.org/abs/2511.03234 - arXiv:2511.03234v1 Announce Type: new -Abstract: We extend the list of tournaments $S$ for which the complete structural description for tournaments excluding $S$ as a subtournament is known. Specifically, let $\Delta(1, 2, 2)$ be a tournament on five vertices obtained from a cyclic triangle by substituting a two-vertex tournament for two of its vertices. In this paper, we show that tournaments excluding $\Delta(1, 2, 2)$ as a subtournament are either isomorphic to one of three small tournaments, obtained from a transitive tournament by reversing edges in vertex-disjoint directed paths, or obtained from a smaller tournament with the same property by applying one of two operations. In particular, one of these operations creates a homogeneous set that induces a subtournament isomorphic to one of three fixed tournaments, and the other creates a homogeneous pair such that their union induces a subtournament isomorphic to a fixed tournament. As an application of this result, we present an upper bound for the chromatic number, a lower bound for the size of a largest transitive subtournament, and a lower bound for the number of vertex-disjoint cyclic triangles for such tournaments. The bounds that we present are all best possible. - oai:arXiv.org:2511.03234v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Seokbeom Kim, Taite LaGrange, Mathieu Rundstr\"om, Arpan Sadhukhan, Sophie Spirkl - - - Computing the nearest $\Omega$-admissible descriptor dissipative Hamiltonian system - https://arxiv.org/abs/2511.03265 - arXiv:2511.03265v1 Announce Type: new -Abstract: For a given set $\Omega \subseteq \mathbb{C}$, a matrix pair $(E,A)$ is called $\Omega$-admissible if it is regular, impulse-free and its eigenvalues lie inside the region $\Omega$. In this paper, we provide a dissipative Hamiltonian characterization for the matrix pairs that are $\Omega$-admissible where $\Omega$ is an LMI region. We then use these results for solving the nearest $\Omega$-admissible matrix pair problem: Given a matrix pair $(E,A)$, find the nearest $\Omega$-admissible pair $(\tilde E, \tilde A)$ to the given pair $(E,A)$. We illustrate our results on several data sets and compare with the state of the art. - oai:arXiv.org:2511.03265v1 - math.NA - cs.NA - cs.SY - eess.SY - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vaishali Aggarwal, Nicolas Gillis, Punit Sharma - - - A decomposition theorem for the Hochschild homology of symmetric powers of a dg category - https://arxiv.org/abs/2511.03269 - arXiv:2511.03269v1 Announce Type: new -Abstract: We prove a conjecture by Belmans, Fu and Krug concerning the Hochschild homology of the symmetric powers of a small dg category $\mathscr{C}$. More precisely, we show that these groups decompose into pieces that only depend on the Hochschild homology of the dg category $\mathscr{C}$. - oai:arXiv.org:2511.03269v1 - math.CT - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Ville Nordstrom - - - Generalized connectedness and Bertini-type theorems over real closed fields - https://arxiv.org/abs/2511.03277 - arXiv:2511.03277v1 Announce Type: new -Abstract: In this paper, we establish a real closed analogue of Bertini's theorem. Let $R$ be a real closed field and $X$ a formally real integral algebraic variety over $R$. We show that if the zero locus of a nonzero global section $s$ of an invertible sheaf on $X$ has a formally real generic point, then $s$ does not change sign on $X$, and vice versa under certain conditions. As a consequence, we demonstrate that there exists a nonempty open subset of hypersurface sections preserving formal reality and integrality for quasi-projective varieties of dimension $\geq 2$ under these conditions. - oai:arXiv.org:2511.03277v1 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Yi Ouyang, Chenhao Zhang - - - A higher rank shifted convolution problem with applications to L-functions - https://arxiv.org/abs/2511.03294 - arXiv:2511.03294v1 Announce Type: new -Abstract: While several instances of shifted convolution problems for GL(3) x GL(2) have been solved, the case where one factor is the classical divisor function and one factor is a GL(3) Fourier coefficient has remained open. We solve this case in the present paper. The proof involves two intertwined applications of different types of delta symbol methods. As an application we establish an asymptotic formula for central values of L-functions for a GL(3) automorphic form twisted by Dirichlet characters to moduli q < Q. - oai:arXiv.org:2511.03294v1 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Valentin Blomer, Junxian Li - - - Technical results on the convergence of quasi-Newton methods for nonsmooth optimization - https://arxiv.org/abs/2511.03296 - arXiv:2511.03296v1 Announce Type: new -Abstract: It is well-known by now that the BFGS method is an effective method for minimizing nonsmooth functions. However, despite its popularity, theoretical convergence results are almost non-existent. One of the difficulties when analyzing the nonsmooth case is the fact that the secant equation forces certain eigenvalues of the quasi-Newton matrix to vanish, which is a behavior that has not yet been fully analyzed. In this article, we show what kind of behavior of the eigenvalues would be sufficient to be able to prove the convergence for piecewise differentiable functions. More precisely, we derive assumptions on the behavior from numerical experiments and then prove criticality of the limit under these assumptions. Furthermore, we show how quasi-Newton methods are able to explore the piecewise structure. While we do not prove that the observed behavior of the eigenvalues actually occurs, we believe that these results still give insight, and a certain intuition, for the convergence for nonsmooth functions. - oai:arXiv.org:2511.03296v1 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Bennet Gebken - - - DRL-Based Robust Multi-Timescale Anti-Jamming Approaches under State Uncertainty - https://arxiv.org/abs/2511.03305 - arXiv:2511.03305v1 Announce Type: new -Abstract: Owing to the openness of wireless channels, wireless communication systems are highly susceptible to malicious jamming. Most existing anti-jamming methods rely on the assumption of accurate sensing and optimize parameters on a single timescale. However, such methods overlook two practical issues: mismatched execution latencies across heterogeneous actions and measurement errors caused by sensor imperfections. Especially for deep reinforcement learning (DRL)-based methods, the inherent sensitivity of neural networks implies that even minor perturbations in the input can mislead the agent into choosing suboptimal actions, with potentially severe consequences. To ensure reliable wireless transmission, we establish a multi-timescale decision model that incorporates state uncertainty. Subsequently, we propose two robust schemes that sustain performance under bounded sensing errors. First, a Projected Gradient Descent-assisted Double Deep Q-Network (PGD-DDQN) algorithm is designed, which derives worst-case perturbations under a norm-bounded error model and applies PGD during training for robust optimization. Second, a Nonlinear Q-Compression DDQN (NQC-DDQN) algorithm introduces a nonlinear compression mechanism that adaptively contracts Q-value ranges to eliminate action aliasing. Simulation results indicate that, compared with the perfect-sensing baseline, the proposed algorithms show only minor degradation in anti-jamming performance while maintaining robustness under various perturbations, thereby validating their practicality in imperfect sensing conditions. - oai:arXiv.org:2511.03305v1 - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Haoqin Zhao, Zan Li, Jiangbo Si, Rui Huang, Hang Hu, Tony Q. S. Quek, Naofal Al-Dhahir - - - The global well-posedness for the Q-tensor model of nematic liquid crystals in the half-space - https://arxiv.org/abs/2511.03309 - arXiv:2511.03309v1 Announce Type: new -Abstract: In this paper, we consider the Q-tensor model of nematic liquid crystals, which couples the Navier-Stokes equations with a parabolic-type equation describing the evolution of the directions of the anisotropic molecules, in the half-space. The aim of this paper is to prove the global well-posedness for the Q-tensor model in the $L_p$-$L_q$ framework. Our proof is based on the Banach fixed point argument. To control the higher-order terms of the solutions, we prove the weighted estimates of the solutions for the linearized problem by the maximal $L_p$-$L_q$ regularity. On the other hand, the estimates for the lower-order terms are obtained by the analytic semigroup theory. Here, the maximal $L_p$-$L_q$ regularity and the generation of an analytic semigroup are provided by the R-solvability for the resolvent problem arising from the Q-tensor model. It seems to be the first result to discuss the unique existence of a global-in-time solution for the Q-tensor model in the half-space. - oai:arXiv.org:2511.03309v1 - math.AP - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Daniele Barbera, Yoshihiro Shibata, Miho Murata - - - Calibration for minimal surfaces with free boundary and Cheeger-type problems - https://arxiv.org/abs/2511.03322 - arXiv:2511.03322v1 Announce Type: new -Abstract: We study a problem of minimal surfaces with free boundary written in the form of a non convex minimization problem. Our aim is to characterize optimal solutions by finding a suitable calibration field. A natural upper bound of the infimum is given by a variant of the Cheeger problem that we solve explicitly proving the optimality thanks to the construction of a cut-locus potential. The comparison with the original problem is then discussed in detail. - oai:arXiv.org:2511.03322v1 - math.AP - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Guy Bouchitt\'e, Minh Phan - - - Constacyclic codes with best-known parameters - https://arxiv.org/abs/2511.03323 - arXiv:2511.03323v1 Announce Type: new -Abstract: In this paper, we construct several infinite families of $q$-ary constacyclic codes over a finite field $\mathbb{F}_q$ with length $n$, dimension around $n/2$, and minimum distance at least $cn/\log_q n$ for some positive constant $c$. They contain many constacyclic codes with optimal, or almost-optimal, or best-known parameters. We also consider various forms of the length $n$. - oai:arXiv.org:2511.03323v1 - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zekai Chen, Min Sha - - - Simplicial Homology Groups - https://arxiv.org/abs/2511.03326 - arXiv:2511.03326v1 Announce Type: new -Abstract: This expository article presents a self-contained introduction to simplicial homology for finite simplicial complexes, emphasizing concrete computation and geometric intuition. Beginning with orientations of simplices and the construction of free abelian chain groups, the boundary operators are defined via the alternating-sum formula and shown to satisfy the chain-complex identity that the boundary of a boundary vanishes. Cycles and boundaries are then developed as kernels and images of the boundary maps, leading to homology groups that capture connected components, independent loops, and higher-dimensional voids. Throughout, detailed low-dimensional examples and step-by-step matrix calculations illustrate how to form boundary matrices, compute kernels and images, and identify generators and relations in \(H_p\). The presentation highlights universal properties of chain groups, clarifies sign conventions and induced orientations, and demonstrates the invariance of homology under combinatorial refinements, thereby connecting geometric features of spaces to computable algebraic invariants. - oai:arXiv.org:2511.03326v1 - math.AT - math.GN - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Sanjay Mishra - - - Calculating generators of power integral bases in sextic fields with a quadratic subfield: the general case - https://arxiv.org/abs/2511.03331 - arXiv:2511.03331v1 Announce Type: new -Abstract: In some previous works we gave algorithms for determining generators of power integral basis in sextic fields with a quadratic subfield, under certain restrictions. The purpose of the present paper is to extend those methods to the general case, when the relative integral basis of the sextic field over the quadratic subfield is of general form. This raises several technical difficulties, that we consider here. - oai:arXiv.org:2511.03331v1 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Istv\'an Ga\'al - - - Conrol-Translated Finsler-type structure and Anisotropic Ginzbor-Landau models - https://arxiv.org/abs/2511.03333 - arXiv:2511.03333v1 Announce Type: new -Abstract: This paper develops a geometric and analytical extension of the Finsler--Ginzburg--Landau framework by introducing a distributed control field acting as a translation in the tangent bundle. Within this formulation, the classical Tonelli Lagrangian is deformed into a control--translated Finsler structure, whose Legendre dual induces a uniformly elliptic operator and a convex energy functional preserving the essential variational features of the anisotropic model. This approach provides a rigorous analytical setting for coupling external control fields with the intrinsic Finsler geometry of anisotropic superconductors. The study establishes the convexity, coercivity, and regularity properties of the induced energy functional and proves the existence of controlled minimizers through variational arguments on admissible configurations. In the asymptotic regime as the Ginzburg--Landau parameter tends to zero, a detailed $\Gamma$--convergence analysis yields a renormalized energy $W_u$ governing vortex interactions under control translation, quantifying the modification of the Green kernel and the self-energy due to the field $u(x)$. The results demonstrate that the control translation preserves the underlying Finsler structure while introducing a new geometric degree of freedom for manipulating and stabilizing vortex configurations. - oai:arXiv.org:2511.03333v1 - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Y. Alipour Fakhri - - - Extension of the Gy\'arf\'as-Sumner conjecture to signed graphs - https://arxiv.org/abs/2511.03335 - arXiv:2511.03335v1 Announce Type: new -Abstract: The balanced chromatic number of a signed graph G is the minimum number of balanced sets that cover all vertices of G. Studying structural conditions which imply bounds on the balanced chromatic number of signed graphs is among the most fundamental problems in graph theory. In this work, we initiate the study of coloring hereditary classes of signed graphs. More precisely, we say that a set F = {F_1, F_2, ..., F_l} is a GS (for Gy\'arf\'as-Sumner) set if there exists a constant c such that signed graphs with no induced subgraph switching equivalent to a member of F admit a balanced c-coloring. The focus of this work is to study GS sets of order 2. We show that if F is a GS set of order 2, then F_1 is either (K_3, -) or (K_4, -), and F_2 is a linear forest. In the case of F_1 = (K_3, -), we show that any choice of a linear forest for F_2 works. In the case of F_1 = (K_4, -), we show that if each connected component of F_2 is a path of length at most 4, then {F_1, F_2} is a GS set. - oai:arXiv.org:2511.03335v1 - math.CO - cs.DM - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Guillaume Aubian, Allen Ibiapina, Luis Kuffner, Reza Naserasr, Cyril Pujol, Cl\'eoph\'ee Robin, Huan Zhou - - - Solutions of Two-stage Stochastic Minimax Problems - https://arxiv.org/abs/2511.03339 - arXiv:2511.03339v1 Announce Type: new -Abstract: This paper introduces a class of two-stage stochastic minimax problems where the first-stage objective function is nonconvex-concave while the second-stage objective function is strongly convex-concave. We establish properties of the second-stage minimax value function and solution functions, and characterize the existence and relationships among saddle points, minimax points, and KKT points. We apply the sample average approximation (SAA) to the class of two-stage stochastic minimax problems and prove the convergence of the KKT points as the sample size tends to infinity. An inexact parallel proximal gradient descent ascent algorithm is proposed to solve this class of problems with the SAA. Numerical experiments demonstrate the effectiveness of the proposed algorithm and validate the convergence properties of the SAA approach. - oai:arXiv.org:2511.03339v1 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hailin Sun, Xiaojun Chen - - - On the piecewise quasipolynomiality of double tropical Welschinger invariants - https://arxiv.org/abs/2511.03342 - arXiv:2511.03342v1 Announce Type: new -Abstract: Ardila and Brugall\'e conjectured that double tropical Welschinger invariants of Hirzebruch surfaces are piecewise quasipolynomial. In this work, we prove the conjecture holds in full generality, i.e. for toric surfaces corresponding to h-transverse polygons. Furthermore, we define new combinatorial Welschinger-type numbers for h-transverse polygons and show that they are likewise piecewise quasipolynomial. - oai:arXiv.org:2511.03342v1 - math.AG - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vincenzo Reda - - - A Spectral Split-Step Pad\'e Method for Guided Wave Propagation - https://arxiv.org/abs/2511.03343 - arXiv:2511.03343v1 Announce Type: new -Abstract: In this study, a Fourier-based, split-step Pad\'e (SSP) method for solving the parabolic wave equation with applications in guided wave propagation in ocean acoustics is presented. Traditional SSP implementations rely in finite-difference discretizations of the depth-dependent differential operator. This approach limits accuracy in coarse discretizations as well as computational efficiency in dense discretizations since it does not significantly benefit from parallelization. In contrast, our proposed method replaces finite differences with a spectral representation using the discrete sine transform (DST). This enables an exact treatment of the vertical operator under homogeneous boundary conditions. For non-constant sound speed, we use a Neumann series expansion to treat inhomogeneities as perturbations. Numerical experiments demonstrate the method's accuracy in range-independent media and rage-dependent scenarios, including propagation in deep ocean with Munk profile and in the presence of a parametrized synoptic eddy. Compared to finite-difference SSP methods, the Fourier-based approach achieves higher accuracy with fewer depth discretization points and avoids the resolution bottleneck associated with sharp field features, making it well-suited for large-scale, high-frequency wave propagation problems in ocean environments. - oai:arXiv.org:2511.03343v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Daniel Walsken, Pavel Petrov, Matthias Ehrhardt - - - Reversibility, covariance and coarse-graining for Langevin dynamics: On the choice of multiplicative noise - https://arxiv.org/abs/2511.03347 - arXiv:2511.03347v1 Announce Type: new -Abstract: We study the interplay between reversibility, geometry, and the choice of multiplicative noise (in particular It\^{o}, Stratonovich, Klimontovich) in stochastic differential equations (SDEs). Building on a unified geometric framework, we derive algebraic conditions under which a diffusion process is reversible with respect to a Gibbs measure on a Riemannian manifold. The condition depends continuously on a parameter $\lambda \in [0,1]$ which interpolates between the conventions of It\^o ($\lambda = 0$), Stratonovich ($\lambda = \frac 1 2$) and Klimontovich ($\lambda = 1$). For reversible slow-fast systems of SDEs with a block-diagonal diffusion structure, we show, using the theory of Dirichlet forms, that both reversibility and the Klimontovich noise interpretation are preserved under coarse-graining. - In particular, we prove that the effective dynamics for the slow variables, obtained via projection onto a lower-dimensional manifold, retain the Klimontovich interpretation and remain reversible with respect to the marginal Gibbs measure/free energy. - Our results provide a flexible variational framework for modeling coarse-grained reversible dynamics with nontrivial geometric and noise structures. - oai:arXiv.org:2511.03347v1 - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Mario Ayala, Nicolas Dirr, Grigorios A. Pavliotis, Johannes Zimmer - - - The hexagonal lattice is universally locally optimal - https://arxiv.org/abs/2511.03353 - arXiv:2511.03353v1 Announce Type: new -Abstract: We prove that the hexagonal lattice is a local minimizer, among all point configurations, of the interaction energy per unit volume for pair potentials that are completely monotonic functions of the square distance. This includes Gaussian interactions and power laws. - oai:arXiv.org:2511.03353v1 - math.MG - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Thomas Lebl\'e - - - Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlev\'e II symmetry reduction - https://arxiv.org/abs/2511.03356 - arXiv:2511.03356v1 Announce Type: new -Abstract: A novel extension of the canonical solitonic mKdV equation is introduced which admits hybrid Ermakov-Painlev\'e II symmetry reduction. Application of the latter is made to obtain exact solution of Airy-type to a class of moving boundary problems of Stefan kind for this extended mKdV equation. A reciprocal transformation is then applied to the latter to generate an associated exactly solvable class of moving boundary problems for an extension of a base Casimir member of a compacton hierachy. The extended mKdV equation is shown to be embedded in a range of nonlinear evolution equations with temporal modulation as determined via the action of a class of involutory transformations with origin in Ermakov theory. Associated temporal modulation for the hybrid mKdV and KdV equation as embedded in the classical solitonic Gardner equation is delimited. - oai:arXiv.org:2511.03356v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Colin Rogers, Adriana C. Briozzo - - - Noise induced Stability of a Mean-Field model of Systemic Risk with uncertain robustness - https://arxiv.org/abs/2511.03358 - arXiv:2511.03358v1 Announce Type: new -Abstract: We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients, corresponding to fluctuations in height of the potential barrier seperating the two wells. This is equivalent to studying a single McKean-Vlasov SDE with explicit dependence on its moments and, novelly, independently varying additive and multiplicative noise. Such non-linear SDEs are known to possess two phases: stable (ordered) and unstable (disordered). When the potential is purely bistable, the phase changes from stable to unstable when noise intensity is increased past a critical threshold. With the recent advances, it will be shown that the behaviour here is far richer: indeed, depending on the interpretation of the stochastic integral, the system exhibits phase changes that cannot occur in any regime where there is no uncertainty in the potential. Strikingly, this allows for the phenomenon of noise induced stability; situations where more noise can reduce the risk of system failure. - oai:arXiv.org:2511.03358v1 - math.PR - q-fin.RM - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-sa/4.0/ - Alexander Alecio - - - Introduction to the theory of mixing for incompressible flows - https://arxiv.org/abs/2511.03360 - arXiv:2511.03360v1 Announce Type: new -Abstract: In these lecture notes, we provide a pedagogical introduction to the theory of mixing for incompressible flows from a PDE perspective. We discuss both the Lagrangian (ODE) and Eulerian (PDE, continuity equation) viewpoints, and introduce suitable notions of mixing scales that quantify the degree to which a scalar field transported by a velocity field becomes mixed. We then address the problem of establishing universal lower bounds on the time evolution of the mixing scale. This is first done in the smooth setting, using energy estimates and flow-based arguments, and later in the Sobolev setting, relying on quantitative estimates for regular Lagrangian flows. Finally, we present recent results concerning the sharpness of these lower bounds, their implications for the geometry and regularity of regular Lagrangian flows, and connections with more recent developments in the literature. - oai:arXiv.org:2511.03360v1 - math.AP - math-ph - math.CA - math.DS - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Gianluca Crippa - - - Pure minimal injective resolutions and perfect modules for lattices - https://arxiv.org/abs/2511.03385 - arXiv:2511.03385v1 Announce Type: new -Abstract: In a recent article, Iyama and Marczinzik showed that a lattice is distributive if and only if the incidence algebra is Auslander regular, giving a new connection between homological algebra and lattice theory. In this article we study when a distributive lattice has a pure minimal injective coresolution, a notion first introduced and studied in a work of Ajitabh, Smith and Zhang. We will see that this problem naturally leads to studying when certain antichain modules are perfect modules. We give a classification of perfect antichain modules under the assumption that their canonical antichain resolution is minimal and use this to give a completion classification in lattice theoretic terms of incidence algebras of distributive lattices with pure minimal injective coresolution. - oai:arXiv.org:2511.03385v1 - math.RT - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tal Gottesman, Vikt\'oria Kl\'asz, Markus Kleinau, Rene Marczinzik - - - Terracini matroids: algebraic matroids of secants and embedded joins - https://arxiv.org/abs/2511.03389 - arXiv:2511.03389v1 Announce Type: new -Abstract: Applications of algebraic geometry have sparked much recent work on algebraic matroids. An algebraic matroid encodes algebraic dependencies among coordinate functions on a variety. - We study the behavior of algebraic matroids under joins and secants of varieties. Motivated by Terracini's lemma, we introduce the notion of a Terracini union of matroids, which captures when the algebraic matroid of a join coincides with the matroid union of the algebraic matroids of its summands. We illustrate applications of our results with a discussion of the implications for toric surfaces and threefolds. - oai:arXiv.org:2511.03389v1 - math.CO - cs.SC - math.AC - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fatemeh Mohammadi, Jessica Sidman, Louis Theran - - - A New Algorithm for Computing the Stabilizing Solution of General Periodic Time-Varying Stochastic Game-Theoretic Riccati Differential Equations - https://arxiv.org/abs/2511.03390 - arXiv:2511.03390v1 Announce Type: new -Abstract: We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer matrix-valued functions iteration sequences, which reformulate the original problem into a set of interconnected bilevel subproblems. By sequentially computing the maximal periodic solutions to the Riccati differential equations associated with each subproblem, we derive the stabilizing periodic solutions for the original problem and rigorously prove the algorithm's convergence. Numerical experiments verifies algorithm effectiveness and stability. This study provides a unified numerical framework for solving a wider range of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations. - oai:arXiv.org:2511.03390v1 - math.NA - cs.NA - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yiyuan Wang - - - A new proof of the Lemmens-Seidel conjecture - https://arxiv.org/abs/2511.03396 - arXiv:2511.03396v1 Announce Type: new -Abstract: In this paper, we give a new proof of the Lemmens-Seidel conjecture on the maximum number of equiangular lines with a common angle $\arccos(1/5)$. This conjecture was previously resolved by Cao, Koolen, Lin, and Yu in 2022 through an analysis involving forbidden subgraphs for the smallest Seidel eigenvalue $-5$. Our new proof is based on bounds on eigenvalue multiplicities of graphs with degree no larger than $14$. To control the maximum degree of the graph associated with equiangular lines, we employ a recent inequality of Balla derived by matrix projection techniques. Our strategy also leads to a new proof for the classical result obtained by Lemmens and Seidel in 1973 for the case where the common angle is $\arccos(1/3)$. - oai:arXiv.org:2511.03396v1 - math.CO - math.MG - math.SP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Chuanyuan Ge, Shiping Liu - - - The (+)-(L, P)-TGRS code - https://arxiv.org/abs/2511.03398 - arXiv:2511.03398v1 Announce Type: new -Abstract: The construction of the non-Reed-Solomon (in short, non-RS) type linear code has been one of the research hotspots in recent years. In 2025, Hu et al. constructed some non-RS MDS codes by defining the (L, P)-twisted generalized Reed-Solomon code (in short, (L, P)-TGRS). In this paper, we focus on the (+)-(L, P)-TGRS code C. We firstly present a parity-check matrix. Secondly, we give a sufficient and necessary condition for C to be NMDS which partially answers two open problems proposed by Hu et al. in 2025, and prove that C is non-RS for 2k > n which partially improves the corresponding result given by Hu et al. in 2025,. Thirdly, we give a sufficient condition for C not to be self-dual or self-orthogonal, respectively, furthermore, we construct two classes of self-orthogonal codes which is a promotion of the corresponding result given by Ding et al. in 2025. Finally, some examples are given. - oai:arXiv.org:2511.03398v1 - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhonghao Liang, Chenlu Jia, Qunying Liao - - - Uniqueness of the second eigenspace of the interchange process - https://arxiv.org/abs/2511.03402 - arXiv:2511.03402v1 Announce Type: new -Abstract: The spectral gap theorem of Caputo, Liggett, and Richthammer states that on any connected graph equipped with edge weights, the 2nd eigenvalue of the interchange process equals the 2nd eigenvalue of the random walk process. In this work we characterize the 2nd eigenspace of the interchange process. We prove that this eigenspace is uniquely determined by the 2nd eigenvectors of the random walk process on every connected weighted graph except the $4$-cycle with uniform edge weights. The key to our proof is an induction scheme on the number of vertices, and involves the octopus (in)equality, representation theoretic computations, and graph Laplacian computations. - oai:arXiv.org:2511.03402v1 - math.PR - math.CO - math.SP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-sa/4.0/ - Dennis Belotserkovskiy, Joe P. Chen - - - Delta invariant of $\mathbb{Q}$-Cartier curve germs and the genus of representable numerical semigroups - https://arxiv.org/abs/2511.03406 - arXiv:2511.03406v1 Announce Type: new -Abstract: In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider representable numerical semigroups, they are semigroups associated with normal weighted homogeneous surface singularities with rational homology sphere links (via the degrees of the homogeneous functions). We then prove that such a semigroup can be interpreted as the value semigroup of a generic orbit (as a curve singularity) given by the $\mathbb{C}^*$-action on the weighted homogeneous germ. Furthermore, we use the delta invariant formula to derive a combinatorially computable formula for the genus of representable semigroups. Finally, we characterize topologically those representable semigroups which are symmetric. - oai:arXiv.org:2511.03406v1 - math.AG - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Zsolt Baja, Tam\'as L\'aszl\'o, Andr\'as N\'emethi - - - On the Fundamental Scaling Laws of Fluid Antenna Systems - https://arxiv.org/abs/2511.03415 - arXiv:2511.03415v1 Announce Type: new -Abstract: Fluid antenna systems (FAS) offer a promising paradigm for enhancing wireless communication by exploiting spatial diversity, yet a rigorous analytical framework for their error probability has been notably absent. To this end, this paper addresses this critical gap by unveiling the \textbf{fundamental scaling laws} that govern the symbol error rate (SER) of FAS in realistic, spatially correlated channels. To establish these laws, we derive a tight, closed-form asymptotic expression for the SER applicable to a general class of modulation schemes. This result is pivotal as it establishes the fundamental scaling law governing the relationship between SER and the channel's spatial correlation structure. Based on this framework, we provide a complete characterization of the diversity and coding gains. The analysis culminates in a definitive design directive: SER can be fundamentally improved by expanding the antenna's movement space to increase diversity, while merely increasing port density within a constrained space yields diminishing returns. - oai:arXiv.org:2511.03415v1 - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xusheng Zhu, Farshad Rostami Ghadi, Tuo Wu, Kaitao Meng, Chao Wang, Gui Zhou - - - Chords of longest cycles in graphs with large circumferences - https://arxiv.org/abs/2511.03422 - arXiv:2511.03422v1 Announce Type: new -Abstract: A long-standing conjecture of Thomassen says that every longest cycle of a $3$-connected graph has a chord. Thomassen (2018) proved that if $G$ is a $2$-connected cubic graph, then any longest cycle must have a chord. He also showed that in any 3-connected graph with minimum degree at least four, some longest cycle must contain a chord. Harvey proved that every longest cycle has a chord for graphs with a large minimum degree. He also conjectured that any longest cycle in a 2-connected graph with minimum degree at least three has a chord. In this paper, we prove that both Thomassen's and Harvey's conjectures are true for graphs with large circumferences. We also prove a more general result for the existence of chords in longest cycles containing a linear forest. - oai:arXiv.org:2511.03422v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Haidong Wu, Shunzhe Zhang - - - Local potential and H\"older estimates for the linearized Monge-Amp\`ere equation - https://arxiv.org/abs/2511.03426 - arXiv:2511.03426v1 Announce Type: new -Abstract: In this paper, we establish local potential estimates and H\"older estimates for solutions of linearized Monge-Amp\`ere equations with the right-hand side being a signed measure, under suitable assumptions on the data. In particular, the interior H\"older estimate holds for an inhomogeneous linearized Monge-Amp\`ere equation with right-hand side being the nonnegative divergence of a bounded vector field in all dimensions. As an application, we give a new approach for the interior estimate of the singular Abreu equation. - oai:arXiv.org:2511.03426v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Guoqing Cui, Ling Wang, Bin Zhou - - - Tropicalization and cluster asymptotic phenomenon of generalized Markov equations - https://arxiv.org/abs/2511.03428 - arXiv:2511.03428v1 Announce Type: new -Abstract: The generalized Markov equations are deeply connected with the generalized cluster algebras of Markov type. We construct a deformed Fock-Goncharov tropicalization for the generalized Markov equations and prove that their tropicalized tree structure is essentially the same as that of the classical Euclid tree. We then define the generalized Euclid tree and prove that it converges to the classical Euclid tree up to a scalar multiple. Moreover, by means of cluster mutations, we exhibit an asymptotic phenomenon, up to some limit q, between the logarithmic generalized Markov tree and the classical Euclid tree. A rationality conjecture of q is then put forward. We also propose a generalized Markov uniqueness conjecture for the generalized Markov equations, which illustrates an application of the asymptotic phenomenon. - oai:arXiv.org:2511.03428v1 - math.NT - math.AC - math.CO - math.RA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhichao Chen, Zelin Jia - - - On metacyclic p-group codes - https://arxiv.org/abs/2511.03429 - arXiv:2511.03429v1 Announce Type: new -Abstract: In this article, we study the metacyclic p-group codes arising from finite semisimple group algebras. In [CM25], we studied group codes arising from metacyclic groups with order divisible by two distinct odd primes. In the current work, we focus on metacyclic p-group codes, as a result of which we are also able to extend the results of [CM25] for metacyclic groups with order divisible by any two primes, not necessarily odd or distinct. Consequently, existing results on group algebras of some important classes of groups, including dihedral and quaternion groups, have been extended. Additionally, we provide left codes for the undertaken group algebras. Finally, we construct non-central codes using units motivated by Bass and bicyclic units, which are inequivalent to any abelian group codes and yield best known parameters. - oai:arXiv.org:2511.03429v1 - math.RA - math.GR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Seema Chahal, Sugandha Maheshwary - - - Helson's conjecture for smooth numbers - https://arxiv.org/abs/2511.03430 - arXiv:2511.03430v1 Announce Type: new -Abstract: Let $\Psi(x,y)$ denote the count of $y$-smooth numbers below $x$ and $P(n)$ denote the largest prime factor of $n$. We prove that for $f$ a Steinhaus random multiplicative function, the partial sums over $y$-smooth numbers enjoy better than squareroot cancellation, in the sense that $$ \mathbb E \Big|\sum_{\substack{1\leq n \leq x\\ P(n) \leq y}} f(n) \Big| = o\left( \Psi(x,y)^{1/2} \right),$$ uniformly for $(\log x)^{30} \leq y \leq x$. Our bounds are quantitative and give a large saving when $y$ isn't too close to $x$. - oai:arXiv.org:2511.03430v1 - math.NT - math.CA - math.CV - math.FA - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Seth Hardy, Max Wenqiang Xu - - - Coincidence among sum formulas for zeta-like multiple values - https://arxiv.org/abs/2511.03431 - arXiv:2511.03431v1 Announce Type: new -Abstract: We study two families of zeta-like multiple series -- the multiple $\rho$-values and the multiple $\eta$-values -- defined by nested sums with shifted denominators. An explicit factorial formula for $\rho$ reveals its intrinsic combinatorial structure and leads to closed expressions for fixed weight and depth. A remarkable identity emerges from a weighted-sum transformation, exhibiting a perfect discrete balance. The main theorem proves that the total sums of $\rho$- and $\eta$-values coincide for equal weight but complementary depths. This correspondence provides an analytic basis for integral representations of $\eta$-values and for deriving weighted sum relations. Together, these results show that the $\rho$- and $\eta$-families form two complementary realizations of a unified analytic-combinatorial structure, bridging factorial and harmonic formulations in zeta-like multiple sums. - oai:arXiv.org:2511.03431v1 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kwang-Wu Chen - - - Categorical construction of Schemes - https://arxiv.org/abs/2511.03433 - arXiv:2511.03433v1 Announce Type: new -Abstract: In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple modules to construct associative schemes. Here, we consider a commutative ring for which we can use the localization in maximal ideals as local moduli. This gives a categorical definition of schemes that is equivalent to the definition in Hartshorne's book, Algebraic Geometry, 1977. The definition includes a construction of the sheaf associated to a presheaf using projective limits, and this makes the basic results in scheme theory more natural. - oai:arXiv.org:2511.03433v1 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Arvid Siqveland - - - Bounds for Banach-Mazur distances between some $C(K)$-spaces - https://arxiv.org/abs/2511.03435 - arXiv:2511.03435v1 Announce Type: new -Abstract: We present several results providing lower bounds for the Banach-Mazur distance \[d_{BM}(C(K), C(L))\] between Banach spaces of continuous functions on compact spaces. The main focus is on the case where $C(L)$ represents the classical Banach space $c$ of convergent sequences. In particular, we obtain generalizations and refinements of recent results from \cite{GP24} and \cite{MP25}. - Currently, it seems that one of the most interesting questions is when $K = [0, \omega]$ is a convergent sequence with a limit and $L = [0,\omega]\times 3$ consists of three convergent sequences. In this case, we obtain \[3.53125 \leq d_{BM}(C([0,\omega]\times 3),C[0,\omega]) \leq 3.87513\] - oai:arXiv.org:2511.03435v1 - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Maciej Korpalski, Grzegorz Plebanek - - - Proximal gradient descent on the smoothed duality gap to solve saddle point problems - https://arxiv.org/abs/2511.03442 - arXiv:2511.03442v1 Announce Type: new -Abstract: In this paper, we minimize the self-centered smoothed gap, a recently introduced optimality measure, in order to solve convex-concave saddle point problems. The self-centered smoothed gap can be computed as the sum of a convex, possibly nonsmooth function and a smooth weakly convex function. Although it is not convex, we propose an algorithm that minimizes this quantity, effectively reducing convex-concave saddle point problems to a minimization problem. Its worst case complexity is comparable to the one of the restarted and averaged primal dual hybrid gradient method, and the algorithm enjoys linear convergence in favorable cases. - oai:arXiv.org:2511.03442v1 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Olivier Fercoq (S2A, LTCI) - - - A Support-Set Algorithm for Optimization Problems with Nonnegative and Orthogonal Constraints - https://arxiv.org/abs/2511.03443 - arXiv:2511.03443v1 Announce Type: new -Abstract: In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our analysis demonstrates that, by fixing the support set, the global solution of the minimization subproblem for the proximal linearization of the objective function can be computed in closed form with at most $n$ nonzero entries. Exploiting this structural property offers a powerful avenue for dramatically enhancing computational efficiency. Guided by this insight, we propose a support-set algorithm preserving strictly the feasibility of iterates. A central ingredient is a strategically devised update scheme for support sets that adjusts the placement of nonzero entries. We establish the global convergence of the support-set algorithm to a first-order stationary point, and show that its iteration complexity required to reach an $\epsilon$-approximate first-order stationary point is $O (\epsilon^{-2})$. Numerical results are strongly in favor of our algorithm in real-world applications, including nonnegative PCA, clustering, and community detection. - oai:arXiv.org:2511.03443v1 - math.OC - cs.LG - stat.ML - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Lei Wang, Xin Liu, Xiaojun Chen - - - Arithmetic invariants of torus links - https://arxiv.org/abs/2511.03446 - arXiv:2511.03446v1 Announce Type: new -Abstract: The classical analogy between knots and primes motivates the study of Alexander polynomials through an arithmetic perspective. In this article we study the two-parameter family of torus knots and links $T_{p,q}$ and analyze the asymptotic behaviour of the zeros of their Alexander polynomials $\Delta_{p,q}(t)$, defined with respect to the total linking number covering. We prove that as $p,q\to\infty$ these zeros become equidistributed on the unit circle and derive an explicit formula for the limiting frequency with which primitive $r$-th roots of unity appear. To capture finer statistical information, we introduce the moment sequence of the zero distribution and compute its generating function in closed form. We further examine the Iwasawa theory of the corresponding branched covers, determining the Iwasawa invariants. The logarithmic Mahler measure of $\Delta_{p,q}(t)$ vanishes identically and the associated homological growth in towers of abelian covers of $S^3$ branched along $T_{p,q}$ is subexponential. - oai:arXiv.org:2511.03446v1 - math.NT - math.GT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Anwesh Ray, Tanushree Shah - - - Rolling carpet strategy to reduce mosquito populations in two-dimensional space - https://arxiv.org/abs/2511.03447 - arXiv:2511.03447v1 Announce Type: new -Abstract: Mosquitoes are vectors of numerous diseases; a strategy to fight the spread of these diseases is to control the vector population. In this article, we focus on the use of the sterile insect technique. Starting from a reaction-diffusion system, we show the existence of 'forced' traveling waves obtained by translating the intervention zone at constant speed. This result is proved in a two-dimensional space by using the radial symmetry. - oai:arXiv.org:2511.03447v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Lu\'is Almeida (SU), Alexis L\'eculier (UB), Nga Nguyen (ENS-PSL), Nicolas Vauchelet - - - A Review of Bilevel Optimization: Methods, Emerging Applications, and Recent Advancements - https://arxiv.org/abs/2511.03448 - arXiv:2511.03448v1 Announce Type: new -Abstract: This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical decision-making situations, where a decision-maker needs to consider a possible response from stakeholder(s) for each of its actions to achieve his own goals. Mathematically, it leads to a nested optimization structure, in which a primary (leader's) optimization problem contains a secondary (follower's) optimization problem as a constraint. Various forms of bilevel problems, including linear, mixed-integer, single-objective, and multi-objective, are covered. For bilevel problem solving methods, various classical and evolutionary approaches are explained. Along with an overview of various areas of applications, two recent considerations of bilevel approach are introduced. The first application involves a bilevel decomposition approach for solving general optimization problems, and the second application involves Neural Architecture Search (NAS), which is a prime example of a bilevel optimization problem in the area of machine learning. - oai:arXiv.org:2511.03448v1 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Dhaval Pujara, Ankur Sinha - - - h-dichotomies via noncritical uniformity and expansiveness for evolution families - https://arxiv.org/abs/2511.03453 - arXiv:2511.03453v1 Announce Type: new -Abstract: In a recent paper (Math. Ann. 393 (2025), 1769--1795), Elorreaga et al. have obtained a complete characterization of the notion of a $h$-dichotomy for ordinary differential equations on a finite-dimensional space in terms of the notions of $h$-expansiveness and $h$-noncriticality. Their results extended the previous results of Coppel and Palmer, which dealt with exponential dichotomies. The main objective of this note is to extend the results of Elorreaga et al. to arbitrary invertible evolution families that act on Banach spaces. We emphasize that our approach is completely different and considerably simpler from the one developed by Elorreaga et al. It is based on the time-rescaling method introduced by Dragicevic and Silva. - oai:arXiv.org:2511.03453v1 - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Davor Dragicevic - - - Hilbert schemes of points on fold-like curves and their combinatorics - https://arxiv.org/abs/2511.03454 - arXiv:2511.03454v1 Announce Type: new -Abstract: We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible components, and provide a detailed analysis of their singularities, revealing rich combinatorial patterns governing its geometry. - oai:arXiv.org:2511.03454v1 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - \'Angel David R\'ios Ortiz, Javier Sendra-Arranz - - - Rational Hodge--Tate prismatic crystals of quasi-l.c.i algebras and non-abelian $p$-adic Hodge theory - https://arxiv.org/abs/2511.03458 - arXiv:2511.03458v1 Announce Type: new -Abstract: Consider a bounded prism $(A,I)$ and a bounded quasi-l.c.i algebra $R$ over $\overline{A}$. In this paper, for any prism $S/A$ with a surjection $S\to R$ such that $\widehat{\mathbb L}_{\overline{S}/\overline{A}}$ is a $p$-completely flat module over $\overline{S}$, we establish an equivalence of categories between rational Hodge-Tate crystals on $(R/A)_{\Delta}$ and topologically nilpotent integrable connections on the Hodge--Tate cohomology ring $\overline{\Delta}_{R/S}$. As an application, for a non-zero divisor $a\in \overline{A}$, we introduce the concept of $a$-smallness for a rational Hodge-Tate prismatic crystal on $(R/A)_{\Delta}$. Finally, we focus on some special algebras $R$ over $\mathcal O_{\mathbb C_p}$ (or generally, the ring of integers of an algebraic closed and complete non-archimedean field) including all $p$-completely smooth algebras, $p$-complete algebras with semi-stable reductions and geometric valuation rings. By using our equivalence, we analyze the restriction functor from the category of $a$-small rational Hodge-Tate prismatic crystals to the category of $v$-vector bundles. This yields some new results in $p$-adic non-abelian Hodge Theory. - oai:arXiv.org:2511.03458v1 - math.NT - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xiaoyu Qu, Jiahong Yu - - - On the non-Archimedean Hitchin map for $\mathrm{SL}_2(F)$ - https://arxiv.org/abs/2511.03469 - arXiv:2511.03469v1 Announce Type: new -Abstract: Let $F$ be a non-Archimedean valued field, $\Sigma$ a closed Riemann surface of genus at least two, and $\Gamma$ its fundamental group. Building on the theory of equivariant harmonic maps into $\mathbb{R}$-trees, we study the non-Archimedean Hitchin map from the $\mathrm{SL}_2(F)$-character variety $\mathcal{X}_F(\Gamma)$, equipped with the non-Archimedean topology, to the space of holomorphic quadratic differentials on $\Sigma$. We prove that this map is continuous and that its image is contained in the space of Jenkins--Strebel differentials. Moreover, we establish a dynamical characterization of unbounded representations, showing that the induced action of $\Gamma$ on the Bruhat--Tits tree of $\mathrm{SL}_2(F)$ is never small. - oai:arXiv.org:2511.03469v1 - math.DG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jiahuang Chen, Siqi He - - - Every group retraction can be realized as a topological retraction - https://arxiv.org/abs/2511.03472 - arXiv:2511.03472v1 Announce Type: new -Abstract: Given a group retraction $r: G \rightarrow H $, we construct a finite topological space $ X_r $ of height 1, together with a topological retraction $\overline{r}: X_r \rightarrow X_r $, such that the group of automorphisms $ \mathrm{Aut}(X_r) $ (or the group of self-homotopy equivalences $ \mathcal{E}(X_r) $) of $X_r$ is isomorphic to $ G $, and $ \mathrm{Aut}(\overline{r}(X_r)) $ (or $\mathcal{E}(\overline{r}(X_r)) $) is isomorphic to $ H$. Moreover, there is a natural map $\overline{r}' : \mathrm{Aut}(X_r) \rightarrow \mathrm{Aut}(\overline{r}(X_r)) $ that coincides with the original group retraction $ r $. As a direct consequence of this construction, we show that height 1 is the minimal height required to realize any finite group as the group of automorphisms (or the group of self-homotopy equivalences) of a finite topological space, except in the case where $ G $ is a symmetric group. In that unique case, the group can be realized by a finite topological space of height 0. - oai:arXiv.org:2511.03472v1 - math.AT - math.GN - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pedro J. Chocano - - - On a Stationarity Theory for Stochastic Volterra Integral Equations - https://arxiv.org/abs/2511.03474 - arXiv:2511.03474v1 Announce Type: new -Abstract: This paper provide a comprehensive analysis of the finite and long time behavior of continuous-time non-Markovian dynamical systems, with a focus on the forward Stochastic Volterra Integral Equations(SVIEs).We investigate the properties of solutions to such equations specifically their stationarity, both over a finite horizon and in the long run. In particular, we demonstrate that such an equation does not exhibit a strong stationary regime unless the kernel is constant or in a degenerate settings. However, we show that it is possible to induce a $\textit{fake stationary regime}$ in the sense that all marginal distributions share the same expectation and variance. This effect is achieved by introducing a deterministic stabilizer $\varsigma$ associated with the kernel.We also look at the $L^p$ -confluence (for $p>0$) of such process as time goes to infinity(i.e. we investigate if its marginals when starting from various initial values are confluent in $L^p$ as time goes to infinity) and finally the functional weak long-run assymptotics for some classes of diffusion coefficients. Those results are applied to the case of Exponential-Fractional Stochastic Volterra Integral Equations, with an $\alpha$-gamma fractional integration kernel, where $\alpha\leq 1$ enters the regime of $\textit{rough path}$ whereas $\alpha> 1$ regularizes diffusion paths and invoke $\textit{long-term memory}$, persistence or long range dependence. With this fake stationary Volterra processes, we introduce a family of stabilized volatility models. - oai:arXiv.org:2511.03474v1 - math.PR - math.DS - q-fin.MF - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Emmanuel Gnabeyeu, Gilles Pag\`es - - - Manivel's semi-group property for Kronecker coefficients, generalized blocks of symmetric groups and Saxl conjecture - https://arxiv.org/abs/2511.03484 - arXiv:2511.03484v1 Announce Type: new -Abstract: Given an positive integer $k$, let $n:=\binom{k+1}{2}$. In 2012, during a talk at UCLA, Jan Saxl conjectured that all irreducible representations of the symmetric group $S_n$ occur in the decomposition of the tensor square of the irreducible representation corresponding to the staircase partition. In this paper, we investigate two useful methods to obtain some irreducible representations that occur in this decomposition. Our main tolls are the semi-group property for Kronecker coefficients and generalized blocks of symmetric groups. - oai:arXiv.org:2511.03484v1 - math.RT - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Mahdi Ebrahimi - - - Dimensional reduction for anyons in the average-field approximation - https://arxiv.org/abs/2511.03491 - arXiv:2511.03491v1 Announce Type: new -Abstract: We study abelian anyons at the mean-field/almost-bosonic level, whose dynamics are governed by the Chern-Simons-Schr\"odinger system. We consider the dimensional reduction of this 2D model by introducing an anisotropic trapping potential, and derive an effective 1D model after tracing out the tight confinement direction. The resulting effective dynamics in the loose confinement direction is captured by a quintic defocusing nonlinear Schr\"odinger equation. We rigorously establish this dimensional reduction process in the sense of ground state energies and time-dependent solutions, under an $H^2$ well-posedness assumption. - oai:arXiv.org:2511.03491v1 - math.AP - cond-mat.mes-hall - cond-mat.quant-gas - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Qiyun Yang - - - A Rernomalisation Group Map for Short- and Long-ranged Weakly Coupled $|\varphi|^4$ Models in $d \ge 4$ at and Above the Critical Point - https://arxiv.org/abs/2511.03495 - arXiv:2511.03495v1 Announce Type: new -Abstract: In this article, we construct and analyse a renormalisation group (RG) map for the weakly coupled $n$-component $|\varphi|^4$ model under periodic boundary conditions in dimension $d \ge 4$. Both short-range and long-range interactions with upper critical dimension four are considered. This extends and refines the RG map constructed by Bauerschmidt, Brydges and Slade for the short-range model at $d=4$. This extension opens the door to establishing the exact decay rate of correlation functions of all of the models discussed. Furthermore, incorporating a large-field decay estimate and comparing with the finite-size scaling results of Michta, Park, and Slade, our analysis provides strong evidence for the emergence of a plateau in systems of finite volume with periodic boundary conditions. - oai:arXiv.org:2511.03495v1 - math.PR - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jiwoon Park - - - A New Model for Compactly Generated Derived Categories of the Second Kind and Curved Koszul Triality - https://arxiv.org/abs/2511.03500 - arXiv:2511.03500v1 Announce Type: new -Abstract: For any curved differential graded algebra $A$, we define a new model structure on the category of curved differential graded $A$-modules, called the injective Guan-Lazarev model structure. We prove that the category of CDG $A$-modules with this model structure is Quillen equivalent to the category of curved differential graded contramodules over the extended bar-construction of $A$, equipped with the contraderived model structure. This result can be seen as bridging the gap between Positselski's theory of conilpotent Koszul triality and Guan-Lazarev's work on non-conilpotent Koszul duality. As an application, we use the injective Guan-Lazarev model structure to show that the tensor product is a Quillen bifunctor with respect to these model structures of the second kind. - oai:arXiv.org:2511.03500v1 - math.CT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Yannick Hoyer, Kristoffer Rank Rasmussen - - - A note on co-Hopfian groups and rings - https://arxiv.org/abs/2511.03505 - arXiv:2511.03505v1 Announce Type: new -Abstract: Let $p$ and $n$ be positive integers. Assume additionally that $p\neq 3$ is a prime and that $n>2$. Let $R$ be a field of characteristic $p$. A very special consequence of a result of Bunina and Kunyavskii (2023, arXiv:2308.10076) is that $SL_{n}(R)$ is co-Hopfian as a group if and only if $R$ is co-Hopfian as a ring. In this paper, we prove that if $k$ is the algebraic closure of the $2$ element field, then $SL_{2}(k)$ is a co-Hopfian group. Since this $k$ is trivially seen to be co-Hopfian as a ring our result somewhat extends that of Bunina and Kunyavskii. We apply our result to prove that the class of groups satisfying Turner's Retract Theorem (called Turner groups here) is not closed under elementary equivalence thereby answering a question posed by the authors in (2017, Comm. Algebra). - oai:arXiv.org:2511.03505v1 - math.GR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Anthony M. Gaglione, Dennis Spellman - - - Uniformisation des surfaces de Riemann - https://arxiv.org/abs/2511.03512 - arXiv:2511.03512v1 Announce Type: new -Abstract: A proof of the uniformization theorem of Riemann surface is given with only elementary properties of holomorphic functions and not using the paracompacity of the surface. This proof leans on an holomorphic version of the topological characterization, due to Brown, of the sphere as variety covered by two discs, a generalization of the construction of double of a Riemann surface with boundary and the arithmetic, due to Jordan, of separation in surfaces - oai:arXiv.org:2511.03512v1 - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Alexis Marin, Dorothea Vienne-Pollak - - - Quasiregular values and cohomology - https://arxiv.org/abs/2511.03514 - arXiv:2511.03514v1 Announce Type: new -Abstract: We prove that the recently shown cohomological obstruction for quasiregular ellipticity has a generalization in the theory of quasiregular values. More specifically, if $M$ is a closed, connected, and oriented Riemannian $n$-manifold, and there exists a map $f \in C(\mathbb{R}^n, M) \cap W^{1,n}_{\mathrm{loc}}(\mathbb{R}^n, M)$ satisfying $\lvert Df(x) \rvert^n \le K J_f(x) + \operatorname{dist}^n(f(x), f(x_0)) \Sigma(x)$ a.e. in $\mathbb{R}^n$ with $K \ge 1$, $x_0 \in \mathbb{R}^n$, and $\Sigma \in L^1(\mathbb{R}^n) \cap L^{1+\varepsilon}_{\mathrm{loc}}(\mathbb{R}^n)$ for some $\varepsilon > 0$, then the real singular cohomology ring $H^*(M; \mathbb{R})$ of $M$ embeds into the exterior algebra $\wedge^* \mathbb{R}^n$ in a graded manner. We also show a partial version of our result for $M$ with dimension greater than $n$, by using a class of maps that combines properties of quasiregular values and quasiregular curves. - oai:arXiv.org:2511.03514v1 - math.DG - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Susanna Heikkil\"a, Ilmari Kangasniemi - - - Explicit Ensemble Learning Surrogate for Joint Chance-Constrained Optimal Power Flow - https://arxiv.org/abs/2511.03515 - arXiv:2511.03515v1 Announce Type: new -Abstract: The increasing penetration of renewable generation introduces uncertainty into power systems, challenging traditional deterministic optimization methods. Chance-constrained optimization offers an approach to balancing cost and risk; however, incorporating joint chance constraints introduces computational challenges. This paper presents an ensemble support vector machine surrogate for joint chance constraint optimal power flow, where multiple linear classifiers are trained on simulated optimal power flow data and embedded as tractable hyperplane constraints via Big--M reformulations. The surrogate yields a polyhedral approximation of probabilistic line flow limits that preserves interpretability and scalability. Numerical experiments on the IEEE 118-bus system show that the proposed method achieves near-optimal costs with a negligible average error of $0.03\%$. These results demonstrate the promise of ensemble surrogates as efficient and transparent tools for risk-aware optimization of power systems. - oai:arXiv.org:2511.03515v1 - math.OC - cs.SY - eess.SY - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Amir Bahador Javadi, Amin Kargarian - - - Spectral theory of dense hypergraph limits - https://arxiv.org/abs/2511.03516 - arXiv:2511.03516v1 Announce Type: new -Abstract: In this work, we develop a spectral theory for hypergraph limits. We prove the convergence of the spectra of adjacency and Laplacian matrices for hypergraph sequences converging in the $1$-cut metric. On the other hand, we give examples of matrix operators associated with hypergraphs whose spectra are not continuous with respect to the $1$-cut metric. Furthermore, we show that these operators are continuous with respect to other cut norms. - oai:arXiv.org:2511.03516v1 - math.CO - math.SP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - \'Agnes Backhausz, Christian Kuehn, Sjoerd van der Niet, Giulio Zucal - - - A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$ - https://arxiv.org/abs/2511.03519 - arXiv:2511.03519v1 Announce Type: new -Abstract: We study the cohomology groups of tautological bundles on Quot schemes over the projective line, which parametrize rank $r$ quotients of a vector bundle $V$ on $\mathbb{P}^1$. Our main result is an analogue of the Borel--Weil--Bott theorem for Quot schemes. As a corollary, we prove recent conjectures of Marian, Oprea, and Sam on the exterior and symmetric powers of tautological bundles. - oai:arXiv.org:2511.03519v1 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Ajay Gautam, Feiyang Lin, Shubham Sinha - - - Model order reduction via Lie groups - https://arxiv.org/abs/2511.03520 - arXiv:2511.03520v1 Announce Type: new -Abstract: Lie groups and their actions are ubiquitous in the description of physical systems, and we explore implications in the setting of model order reduction (MOR). We present a novel framework of MOR via Lie groups, called MORLie, in which high-dimensional dynamical systems on manifolds are approximated by low-dimensional dynamical systems on Lie groups. In comparison to other Lie group methods we are able to attack non-equivariant dynamics, which are frequent in practical applications, and we provide new non-intrusive MOR methods based on the presented geometric formulation. We also highlight numerically that MORLie has a lower error bound than the Kolmogorov $N$-width, which limits linear-subspace methods. The method is applied to various examples: 1. MOR of a simplified deforming body modeled by a noisy point cloud data following a sheering motion, where MORLie outperforms a naive POD approach in terms of accuracy and dimensionality reduction. 2. Reconstructing liver motion during respiration with data from edge detection in ultrasound scans, where MORLie reaches performance approaching the state of the art, while reducing the training time from hours on a computing cluster to minutes on a mobile workstation. 3. An analytic example showing that the method of freezing is analytically recovered as a special case, showing the generality of the geometric framework. - oai:arXiv.org:2511.03520v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Yannik P. Wotte, Patrick Buchfink, Silke Glas, Federico Califano, Stefano Stramigioli - - - HJB equations driven by the Dirichlet-Ferguson Laplacian in Wasserstein-Sobolev spaces - https://arxiv.org/abs/2511.03522 - arXiv:2511.03522v1 Announce Type: new -Abstract: We study linear and nonlinear PDEs defined on the space of $\mathcal{P}(\mathbb{T}^d)$ over the flat torus $\mathbb{T}^d$, equipped with the Dirichlet-Ferguson measure $\mathcal{D}$. We first develop an analytic framework based on the Wasserstein-Sobolev space $H^{1,2}(\mathcal{P}(\mathbb{T}^d), W_2, \mathcal{D})$ associated with the Dirichlet form induced by the infinite-dimensional Laplacian acting on functions of measures. Within this setting, we establish existence and uniqueness results for transport-diffusion and Hamilton-Jacobi equations in the Wasserstein space. Our analysis connects the PDE approach with a corresponding interacting particles system providing a probabilistic (Kolmogorov-type) representation of strong solutions. Finally, we extend the theory to semilinear equations and mean-field optimal control problems, together with consistent finite-dimensional approximations. - oai:arXiv.org:2511.03522v1 - math.OC - math.AP - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Fran\c{c}ois Delarue, Mattia Martini, Giacomo Enrico Sodini - - - Lie $n$-centralizers of von Neumann algebras - https://arxiv.org/abs/2511.03523 - arXiv:2511.03523v1 Announce Type: new -Abstract: Let $\U$ be a von Neumann algebra with a projection $P\in \U$. For any $A_1,A_2,\ldots,A_n\in\U,$ define $p_1(A_1)=A_1,$ $p_n (A_1,A_2,\ldots,A_n)=[p_{n-1} (A_1,A_2,\ldots,A_{n-1}),A_n]$ for all integers $n\geq 2,$ where $[A,B]=AB-BA$ $(A,B\in\U)$ denotes the usual Lie product. Assume that $\phi:\U\to\U$ is an additive mapping satisfying \[\phi(p_n(A_1, A_2, \ldots, A_n)) = p_n(\phi(A_1), A_2, \ldots, A_n) = p_n(A_1, \phi(A_2), \ldots, A_n) \] for all $A_1, A_2, \ldots, A_n \in \U$ with $A_1A_2=P$ In this article, it is shown that the map $\phi$ is of the form $\phi(A)=WA+\xi(A)$ for all $A\in \U$, where $W\in \mathrm{Z}(\U)$, and $\xi:\U \to \Z(\U)$ ($\Z(\U)$ is the center of $\U$) is an additive map such that $\xi(p_n(A_1, A_2, \ldots, A_n) )=0$ for any $A_1, A_2, \ldots, A_n \in \U$ with $A_1A_2=P$. As an application, we characterize generalized Lie $n$-derivations on arbitrary von Neumann algebras. - oai:arXiv.org:2511.03523v1 - math.OA - math.RA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Mohammad Ashraf, Mohammad Afajal Ansari, Md Shamim Akhter, Feng Wei - - - Counterexamples to statements on isometric graph coverings - https://arxiv.org/abs/2511.03524 - arXiv:2511.03524v1 Announce Type: new -Abstract: A connected subgraph of a graph is isometric if it preserves distances. In this short note, we provide counterexamples to several variants of the following general question: When a graph $G$ is edge covered by connected isometric subgraphs $H_1,\dots,H_k$, which properties of $G$ can we infer from properties of $H_1,\dots,H_k$? For example, Dumas, Foucaud, Perez and Todinca (SIDMA, 2024) proved that when $H_1,\dots,H_k$ are paths, then the pathwidth of $G$ is bounded in terms of $k$. Among others, we show that there are graphs of arbitrarily large treewidth that can be isometrically edge covered by four trees. - oai:arXiv.org:2511.03524v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Paul Bastide, Julien Duron, J\k{e}drzej Hodor, Weichan Liu, Xiangxiang Nie - - - Rational normal curves as no-$(d+2)$-on-$Q$-quadric sets - https://arxiv.org/abs/2511.03526 - arXiv:2511.03526v1 Announce Type: new -Abstract: For every $d\geq 2$, we construct a subset $D\subseteq \{1,2,\dots,n\}^d$ of size $n-o(n)$ such that every affine hyperplane of $\mathbb{R}^d$ intersects $D$ in at most $d$ points, and every hypersphere of $\mathbb{R}^n$ intersects $D$ in at most $d+1$ points. This construction is the largest one currently known, and strongly builds on ideas of Dong, Xu, and also of Thiele. More generally, we prove that the role of hyperspheres can be replaced by $Q$-quadrics, i.e. by quadratic surfaces given by an equation whose degree two homogeneous part equals a fixed quadratic form $Q$. We formulate analogous statements in affine spaces over (finite) fields. Essentially, every construction is given by a suitable rational normal curve in a $d$-dimensional projective space. - oai:arXiv.org:2511.03526v1 - math.CO - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - D\'avid R. Szab\'o - - - Orbifold Bogomolov-Gieseker inequalities on compact K\"ahler varieties - https://arxiv.org/abs/2511.03530 - arXiv:2511.03530v1 Announce Type: new -Abstract: In a previous paper, the orbifold Bogomolov-Gieseker inequality is proved for a stable reflexive sheaf on a compact K\"ahler variety with klt singularities. In this paper, we give a characterization on the stable reflexive sheaf when the Bogomolov-Gieseker equality holds. - oai:arXiv.org:2511.03530v1 - math.DG - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Xin Fu, Wenhao Ou - - - Curvature Decay and the Spectrum of the Non-Abelian Laplacian on R^3 - https://arxiv.org/abs/2511.03532 - arXiv:2511.03532v1 Announce Type: new -Abstract: I study the spectral behavior of the covariant Laplacian $\Delta_A = d_A^* d_A$ associated with smooth $\mathrm{SU}(2)$ connections on $\mathbb{R}^3$. The main result establishes a sharp threshold for the pointwise decay of curvature governing the essential spectrum of $\Delta_A$. Specifically, if the curvature satisfies the bound $|F_A(x)| \le C(1 + |x|)^{-3-\varepsilon}$ for some $\varepsilon > 0$, then $\Delta_A$ is a relatively compact perturbation of the flat Laplacian and hence $\sigma_{\mathrm{ess}}(\Delta_A) = [0,\infty)$. At the critical decay rate $|F_A(x)| \sim |x|^{-3}$, I construct a smooth connection for which $0 \in \sigma_{\mathrm{ess}}(\Delta_A)$, showing that the threshold is sharp. Moreover, a genuinely non-Abelian example based on the hedgehog ansatz is given to demonstrate that the commutator term $A \wedge A$ contributes at the same order. This work identifies the exact decay rate separating stable preservation of the essential spectrum from the onset of delocalized modes in the non-Abelian setting, providing a counterpart to classical results on magnetic Schr\"odinger operators. - oai:arXiv.org:2511.03532v1 - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Michael Wilson - - - Asymptotics of the maximum likelihood estimator of the location parameter of Pearson Type VII distribution - https://arxiv.org/abs/2511.03535 - arXiv:2511.03535v1 Announce Type: new -Abstract: We study the maximum likelihood estimator of the location parameter of the Pearson Type VII distribution with known scale. We rigorously establish precise asymptotic properties such as strong consistency, asymptotic normality, Bahadur efficiency and asymptotic variance of the maximum likelihood estimator. Our focus is the heavy-tailed case, including the Cauchy distribution. The main difficulty lies in the fact that the likelihood equation may have multiple roots; nevertheless, the maximum likelihood estimator performs well for large samples. - oai:arXiv.org:2511.03535v1 - math.ST - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Kazuki Okamura - - - Polynomial identities for quivers via incidence algebras - https://arxiv.org/abs/2511.03536 - arXiv:2511.03536v1 Announce Type: new -Abstract: We show that the path algebra of a quiver satisfies the same polynomial identities of an algebra of matrices, if any. In particular, the algebra of nxn matrices is PI-equivalent to the path algebra of the oriented cycle with n vertices. - oai:arXiv.org:2511.03536v1 - math.RT - math.CO - math.RA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Allan Berele, Giovanni Cerulli Irelli, Javier De Loera Ch\'avez, Elena Pascucci - - - Convexity of the K-energy and Uniqueness of Extremal metrics - An Expository Introduction - https://arxiv.org/abs/2511.03544 - arXiv:2511.03544v1 Announce Type: new -Abstract: This article is an expository introduction to our paper Convexity of the K-energy and Uniqueness of Extremal metrics. We present the main ideas behind the proof that Mabuchi's K-energy functional is convex along weak geodesics in the space of Kahler potentials and explain how this leads to the uniqueness of constant scalar curvature Kahler metrics and extremal metrics up to automorphisms. The emphasis is on the conceptual framework and key techniques. - oai:arXiv.org:2511.03544v1 - math.DG - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Robert J. Berman, Bo Berndtsson - - - The Structure of Cross-Validation Error: Stability, Covariance, and Minimax Limits - https://arxiv.org/abs/2511.03554 - arXiv:2511.03554v1 Announce Type: new -Abstract: Despite ongoing theoretical research on cross-validation (CV), many theoretical questions about CV remain widely open. This motivates our investigation into how properties of algorithm-distribution pairs can affect the choice for the number of folds in $k$-fold cross-validation. - Our results consist of a novel decomposition of the mean-squared error of cross-validation for risk estimation, which explicitly captures the correlations of error estimates across overlapping folds and includes a novel algorithmic stability notion, squared loss stability, that is considerably weaker than the typically required hypothesis stability in other comparable works. - Furthermore, we prove: - 1. For every learning algorithm that minimizes empirical error, a minimax lower bound on the mean-squared error of $k$-fold CV estimating the population risk $L_\mathcal{D}$: \[ \min_{k \mid n}\; \max_{\mathcal{D}}\; \mathbb{E}\!\left[\big(\widehat{L}_{\mathrm{CV}}^{(k)} - L_{\mathcal{D}}\big)^{2}\right] \;=\; \Omega\!\big(\sqrt{k}/n\big), \] where $n$ is the sample size and $k$ the number of folds. This shows that even under idealized conditions, for large values of $k$, CV cannot attain the optimum of order $1/n$ achievable by a validation set of size $n$, reflecting an inherent penalty caused by dependence between folds. - 2. Complementing this, we exhibit learning rules for which \[ - \max_{\mathcal{D}}\; \mathbb{E}\!\left[\big(\widehat{L}_{\mathrm{CV}}^{(k)} - L_{\mathcal{D}}\big)^{2}\right] \;=\; \Omega(k/n), \] matching (up to constants) the accuracy of a hold-out estimator of a single fold of size $n/k$. - Together these results delineate the fundamental trade-off in resampling-based risk estimation: CV cannot fully exploit all $n$ samples for unbiased risk evaluation, and its minimax performance is pinned between the $k/n$ and $\sqrt{k}/n$ regimes. - oai:arXiv.org:2511.03554v1 - math.ST - cs.LG - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ido Nachum, R\"udiger Urbanke, Thomas Weinberger - - - Simplex inequalities of order and chain polytopes of recursively defined posets - https://arxiv.org/abs/2511.03557 - arXiv:2511.03557v1 Announce Type: new -Abstract: In this paper, we study the simplex faces of the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a finite poset $P$. We show that, if $P$ can be recursively constructed from $\mathbf{X}$-free posets using disjoint unions and ordinal sums, then $\mathcal{C}(P)$ has at least as many $k$-dimensional simplex faces as $\mathcal{O}(P)$ does, for each dimension $k$. This generalizes a previous result of Mori, both in terms of the dimensions of the simplices and in terms of the class of posets considered. - oai:arXiv.org:2511.03557v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ragnar Freij-Hollanti, Teemu Lundstr\"om - - - Improving Directions in Mixed Integer Bilevel Linear Optimization - https://arxiv.org/abs/2511.03566 - arXiv:2511.03566v1 Announce Type: new -Abstract: We consider the central role of improving directions in solution methods for mixed integer bilevel linear optimization problems (MIBLPs). Current state-of-the-art methods for solving MIBLPs employ the branch-and-cut framework originally developed for solving mixed integer linear optimization problems. This approach relies on oracles for two kinds of subproblems: those for checking whether a candidate pair of leader's and follower's decisions is bilevel feasible, and those required for generating valid inequalities. Typically, these two types of oracles are managed separately, but in this work, we explore their close connection and propose a solution framework based on solving a single type of subproblem: determining whether there exists a so-called improving feasible direction for the follower's problem. Solution of this subproblem yields information that can be used both to check feasibility and to generate strong valid inequalities. Building on prior works, we expose the foundational role of improving directions in enforcing the follower's optimality condition and extend a previously known hierarchy of optimality-based relaxations to the mixed-integer setting, showing that the associated relaxed feasible regions coincide exactly with the closure associated with intersection cuts derived from improving directions. Numerical results with an implementation using a modified version of the open source solver MibS show that this approach can yield practical improvements. - oai:arXiv.org:2511.03566v1 - math.OC - cs.MS - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Federico Battista, Ted K. Ralphs - - - Exploiting Over-Approximation Errors as Preview Information for Nonlinear Control - https://arxiv.org/abs/2511.03577 - arXiv:2511.03577v1 Announce Type: new -Abstract: We study the control of nonlinear constrained systems via over-approximations. Our key observation is that the over-approximation error, rather than being an unknown disturbance, can be exploited as input-dependent preview information. This leads to the notion of informed policies, which depend on both the state and the error. We formulate the concretization problem -recovering a valid input for the true system from a preview-based policy- as a fixed-point equation. Existence of solutions follows from the Brouwer fixed-point theorem, while efficient computation is enabled through closed-form, linear, or convex programs for input-affine systems, and through an iterative method based on the Banach fixed-point theorem for nonlinear systems. - oai:arXiv.org:2511.03577v1 - math.OC - cs.SY - eess.SY - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Antoine Aspeel, Antoine Girard, Thiago Alves Lima - - - The Weyl law for the Dirichlet Laplacian - https://arxiv.org/abs/2511.03584 - arXiv:2511.03584v1 Announce Type: new -Abstract: The purpose of this paper is to review the asymptotic distribution of eigenvalues of the Dirichlet Laplacian. We introduce and recall all the relevant spectral quantities and provide a proof based on the Fourier Tauberian Theorem. - oai:arXiv.org:2511.03584v1 - math.SP - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alessandro Pietro Contini - - - Characterizations of undirected 2-quasi best match graphs - https://arxiv.org/abs/2511.03592 - arXiv:2511.03592v1 Announce Type: new -Abstract: Bipartite best match graphs (BMG) and their generalizations arise in mathematical phylogenetics as combinatorial models describing evolutionary relationships among related genes in a pair of species. In this work, we characterize the class of \emph{undirected 2-quasi-BMGs} (un2qBMGs), which form a proper subclass of the $P_6$-free chordal bipartite graphs. We show that un2qBMGs are exactly the class of bipartite graphs free of $P_6$, $C_6$, and the eight-vertex Sunlet$_4$ graph. Equivalently, a bipartite graph $G$ is un2qBMG if and only if every connected induced subgraph contains a ``heart-vertex'' which is adjacent to all the vertices of the opposite color. We further provide a $O(|V(G)|^3)$ algorithm for the recognition of un2qBMGs that, in the affirmative case, constructs a labeled rooted tree that ``explains'' $G$. Finally, since un2qBMGs coincide with the $(P_6,C_6)$-free bi-cographs, they can also be recognized in linear time. - oai:arXiv.org:2511.03592v1 - math.CO - cs.DM - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Annachiara Korchmaros, Guillaume E. Scholz, Peter F. Stadler - - - Adaptive Randomized Tensor Train Rounding using Khatri-Rao Products - https://arxiv.org/abs/2511.03598 - arXiv:2511.03598v1 Announce Type: new -Abstract: Approximating a tensor in the tensor train (TT) format has many important applications in scientific computing. Rounding a TT tensor involves further compressing a tensor that is already in the TT format. This paper proposes new randomized algorithms for TT-rounding that uses sketches based on Khatri-Rao products (KRP). When the TT-ranks are known in advance, the proposed methods are comparable in cost to the sketches that used a sketching matrix in the TT-format~\cite{al2023randomized}. However, the use of KRP sketches enables adaptive algorithms to round the tensor in the TT-format within a fixed user-specified tolerance. An important component of the adaptivity is the estimation of error using KRP sketching, for which we develop theoretical guarantees. We report numerical experiments on synthetic tensors, parametric low-rank kernel approximations, and the solution of parametric partial differential equations. The numerical experiments show that we obtain speed-ups of up to $50\times$ compared to deterministic TT-rounding. Both the computational cost analysis and numerical experiments verify that the adaptive algorithms are competitive with the fixed rank algorithms, suggesting the adaptivity introduces only a low overhead. - oai:arXiv.org:2511.03598v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Hussam Al Daas, Grey Ballard, Laura Grigori, Mariana Martinez Aguilar, Arvind K. Saibaba, Bhisham Dev Verma - - - The noncommutative weak Extension Principle - https://arxiv.org/abs/2511.03607 - arXiv:2511.03607v1 Announce Type: new -Abstract: We introduce and study the noncommutative weak Extension Principle, a lifting principle aiming to characterise $^*$-homomorphisms between coronas of nonunital separable $\mathrm{C}^*$-algebras. While this principle fails if the Continuum Hypothesis is assumed, we show that this principle holds under mild forcing axioms such as the Open Colouring Axiom and Martin's Axiom. Further, we introduce and study the notion of nonmeagre ideals in multipliers and coronas of noncommutative $\mathrm{C}^*$-algebras, generalising the usual notion of nonmeagre ideals in $\mathcal P(\mathbb N)$. - oai:arXiv.org:2511.03607v1 - math.LO - math.OA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alessandro Vignati, Deniz Yilmaz - - - Some Applications of Arutyunov Mordukhovich Zhukovskiy Theorem to Stochastic Integral Equations - https://arxiv.org/abs/2511.03623 - arXiv:2511.03623v1 Announce Type: new -Abstract: Mordukhovich derivatives (Mordukhovich coderivatives) of set-valued mappings in Banach spaces have firmly laid the foundation of the theory of generalized differentiation in set-valued analysis, which has been widely applied to optimization theory, equilibrium theory, variational analysis, and so forth, with respect to set-valued mappings. One of the most important applications of Mordukhovich derivatives is to define the covering constants for set-valued mappings in Banach spaces, which play an important role in the well-known Arutyunov Mordukhovich Zhukovskiy Parameterized Coincidence Point Theorem (Theorem 3.1 in [1]). In [15], this theorem is simply named as AMZ Theorem. In this paper, we consider locally or globally stochastic infinitely dimensional systems of linear equations in lp space. We use the Mordukhovich derivatives to precisely find the covering constants for linear and continuous mappings in lp spaces. Then, by using the AMZ Theorem, we prove an existence theorem for solutions to some locally or globally stochastic infinitely dimensional systems of linear functional equations in lp spaces and an existence theorem for solutions to some stochastic integral equations - oai:arXiv.org:2511.03623v1 - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Jinlu Li - - - Critical sinh-Gordon flow with non-negative weight functions - https://arxiv.org/abs/2511.03624 - arXiv:2511.03624v1 Announce Type: new -Abstract: The aim of this article is twofold: one one side we introduce and study the properties of a critical sinh-Gordon type flow \begin{equation*} {\frac{\partial}{\partial t}}e^u=\Delta_gu+8\pi\left({\frac{h_1e^u}{\int_{\Sigma}h_1e^udV_g}}-1\right)-\rho_2\left({\frac{h_2e^{-u}}{\int_{\Sigma}h_2e^{-u}dV_g}}-1\right), \end{equation*} where $\rho_2<8\pi$, $h_1,h_2$ are non-negative weight functions and $\Sigma$ is a closed Riemannian surface. Secondly, under suitable geometric conditions, we prove the convergence of the flow to a solution of the critical sinh-Gordon equation, extending the result of Zhou (2008) to the case of non-negative weights. The argument is based on a careful blow-up analysis. Some remarks about a Toda flow are also given. - oai:arXiv.org:2511.03624v1 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Qiang Fei, Aleks Jevnikar, Sang-Hyuck Moon - - - Notes on generalised spin structures - https://arxiv.org/abs/2511.03627 - arXiv:2511.03627v1 Announce Type: new -Abstract: We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop a covariant Cartan calculus. We introduce an extension of the Lie algebra of Killing vectors, the symmetry algebra, and show that it has a representation on sections of associated bundles. We discuss homogeneous generalised spin structures and provide a characterisation of them in terms of lifts of the isotropy representation. - oai:arXiv.org:2511.03627v1 - math.DG - hep-th - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Andrew D. K. Beckett - - - Neural Beamforming with Doppler-Aware Sparse Attention for High Mobility Environments - https://arxiv.org/abs/2511.03632 - arXiv:2511.03632v1 Announce Type: new -Abstract: Beamforming has significance for enhancing spectral efficiency and mitigating interference in multi-antenna wireless systems, facilitating spatial multiplexing and diversity in dense and high mobility scenarios. Traditional beamforming techniques such as zero-forcing beamforming (ZFBF) and minimum mean square error (MMSE) beamforming experience performance deterioration under adverse channel conditions. Deep learning-based beamforming offers an alternative with nonlinear mappings from channel state information (CSI) to beamforming weights by improving robustness against dynamic channel environments. Transformer-based models are particularly effective due to their ability to model long-range dependencies across time and frequency. However, their quadratic attention complexity limits scalability in large OFDM grids. Recent studies address this issue through sparse attention mechanisms that reduce complexity while maintaining expressiveness, yet often employ patterns that disregard channel dynamics, as they are not specifically designed for wireless communication scenarios. In this work, we propose a Doppler-aware Sparse Neural Network Beamforming (Doppler-aware Sparse NNBF) model that incorporates a channel-adaptive sparse attention mechanism in a multi-user single-input multiple-output (MU-SIMO) setting. The proposed sparsity structure is configurable along 2D time-frequency axes based on channel dynamics and is theoretically proven to ensure full connectivity within p hops, where p is the number of attention heads. Simulation results under urban macro (UMa) channel conditions show that Doppler-aware Sparse NNBF significantly outperforms both a fixed-pattern baseline, referred to as Standard Sparse NNBF, and conventional beamforming techniques ZFBF and MMSE beamforming in high mobility scenarios, while maintaining structured sparsity with a controlled number of attended keys per query. - oai:arXiv.org:2511.03632v1 - cs.IT - cs.LG - eess.SP - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Cemil Vahapoglu, Timothy J. O'Shea, Wan Liu, Sennur Ulukus - - - Wasserstein Rigidity over $\mathbb{R}^n$ with smooth norms - https://arxiv.org/abs/2511.03640 - arXiv:2511.03640v1 Announce Type: new -Abstract: We study $p-$Wasserstein spaces $ \mathcal{W}_p(\mathbb{R}^n, d_N)$ over $\mathbb{R}^n$ equipped with a norm metric $d_N$. We show that, if the norm is smooth enough, then the Wasserstein space is isometrically rigid whenever $p \neq 2$. We also show that, even when $p=2$, we can recover the isometric rigidity of the Wasserstein space $\mathcal{W}_2(\mathbb{R}^n, d_N)$ when $N$ is an $l_q-$norm and $q>2$. - oai:arXiv.org:2511.03640v1 - math.MG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zolt\'an M. Balogh, Eric Str\"oher, Tam\'as Titkos, D\'aniel Virosztek - - - Geometrically robust least squares through manifold optimization - https://arxiv.org/abs/2511.03644 - arXiv:2511.03644v1 Announce Type: new -Abstract: This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization problem on a product manifold, where one variable is constrained to a ball describing uncertainty. To handle the constraint, an exact penalty method is applied. A first-order gradient descent ascent algorithm is proposed to solve the problem, and its convergence properties are illustrated by an example. The proposed method offers a robust approach to solving a wide range of problems arising in signal processing and data-driven control. - oai:arXiv.org:2511.03644v1 - math.OC - cs.SY - eess.SY - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Jeremy Coulson, Alberto Padoan, Cyrus Mostajeran - - - Knotted surfaces, Homological Norm and Extendable Subgroup - https://arxiv.org/abs/2511.03648 - arXiv:2511.03648v1 Announce Type: new -Abstract: We prove that for arbitrary g, there is a surface K of genus g embedded in S4, which has finitely many extendable self-homeomorphisms' action on H1(K,Z), by defining a norm on H1(K,Z) and proving its additivity. - oai:arXiv.org:2511.03648v1 - math.GN - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - 10.1016/j.topol.2025.109644 - Qiling Liu, Knotted surfaces, homological norm and extendable subgroup, Top. and its App 377(2026), 1-6 - Qiling Liu - - - The Heisenberg algebra of a vector space and Hochschild homology - https://arxiv.org/abs/2511.03649 - arXiv:2511.03649v1 Announce Type: new -Abstract: We decategorify the Heisenberg 2-category of Gyenge-Koppensteiner-Logvinenko using Hochschild homology. We use this to generalise the Heisenberg algebra action of Grojnowski and Nakajima to all smooth and proper noncommutative varieties in the noncommutative geometry setting proposed by Kontsevich and Soibelman. For ordinary commutative varieties, we compute the resulting action on Chen-Ruan orbifold cohomology. As tools, we prove results about Heisenberg algebras of a graded vector space which might be of independent interest. - oai:arXiv.org:2511.03649v1 - math.AG - math.CT - math.RT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - \'Ad\'am Gyenge, Timothy Logvinenko - - - Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation - https://arxiv.org/abs/2511.03654 - arXiv:2511.03654v1 Announce Type: new -Abstract: We analyse the momentum distribution of a three-dimensional Fermi gas in the mean-field scaling regime in a trial state that was recently proven to reproduce the Gell-Mann-Brueckner correlation energy for Coulomb potentials. For a class of potentials including the Coulomb potential we show that the momentum distribution is given by a step profile corrected by a random phase approximation contribution as predicted by Daniel and Vosko. Moreover, for potentials with summable Fourier transform we provide optimal error bounds for the deviation from the random phase approximation. This refines a recent analysis by two of the authors to the physically most relevant potentials and to momenta closer to the Fermi surface. - oai:arXiv.org:2511.03654v1 - math-ph - cond-mat.quant-gas - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Niels Benedikter, Sascha Lill, Diwakar Naidu - - - SIMD-vectorized implicit symplectic integrators can outperform explicit ones - https://arxiv.org/abs/2511.03655 - arXiv:2511.03655v1 Announce Type: new -Abstract: The main purpose of this work is to present a SIMD-vectorized implementation of the symplectic 16th-order 8-stage implicit Runge-Kutta integrator based on collocation with Gauss-Legendre nodes (IRKGL16-SIMD), and to show that it can outperform state-of-the-art symplectic explicit integrators for high-precision numerical integrations (in double-precision floating-point arithmetic) of non-stiff Hamiltonian ODE systems. Our IRKGL16-SIMD integrator leverages Single Instruction Multiple Data (SIMD) based parallelism (in a way that is transparent to the user) to significantly enhance the performance of the sequential IRKGL16 implementation. We present numerical experiments comparing IRKGL16-SIMD with state-of-the-art high-order explicit symplectic methods for the numerical integration of several Hamiltonian systems in double-precision floating-point arithmetic. - oai:arXiv.org:2511.03655v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Mikel Anto\~nana, Joseba Makazaga, Ander Murua - - - Left Inverses for B-spline Subdivision Matrices in Tensor-Product Spaces - https://arxiv.org/abs/2511.03658 - arXiv:2511.03658v1 Announce Type: new -Abstract: In this article, we study dyadic coarsening operators in univariate spline spaces and in tensor-product spline spaces over uniform grids. Our construction is strongly motivated by the work of Bartels, Golub, and Samavati (2006), Some observations on local least squares, BIT, 46(3):455--477. The proposed operators are local in nature and yield approximations to a given spline that are comparable to the global L2-best approximation, while being significantly faster to compute and computationally inexpensive. - oai:arXiv.org:2511.03658v1 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Marcelo Actis, Silvano Figueroa, Eduardo M. Garau - - - Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs - https://arxiv.org/abs/2511.03668 - arXiv:2511.03668v1 Announce Type: new -Abstract: Every graph G can be embedded in a Euclidean space as a two-distance set. This allows us to reformulate the analogue of Borsuk's conjecture for two-distance sets in terms of graphs. This conjecture remains open for dimensions from 4 to 63. This short note also discusses an approach for finding counterexamples using graphs, as well as its generalization for s-distance sets. - oai:arXiv.org:2511.03668v1 - math.CO - math.MG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Oleg R. Musin - - - Uniqueness of the measure of maximal entropy for geodesic flows on coarse hyperbolic manifolds without conjugate points - https://arxiv.org/abs/2511.03672 - arXiv:2511.03672v1 Announce Type: new -Abstract: In this article we study geodesic flows on closed Riemannian manifolds without conjugate points and divergence property of geodesic rays. If the fundamental group is Gromov hyperbolic and residually finite we prove, under appropriate assumptions on the expansive set, that the geodesic flow has a unique measure of maximal entropy. This generalizes corresponding results of Climenhaga, Knieper and War proved under the stronger assumption of the existence of a background metric of negative sectional curvature. - oai:arXiv.org:2511.03672v1 - math.DS - math.DG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gerhard Knieper - - - Blossoming bijection for bipartite maps: a new approach via orientations and applications to the Ising model - https://arxiv.org/abs/2511.03680 - arXiv:2511.03680v1 Announce Type: new -Abstract: We develop a new bijective framework for the enumeration of bipartite planar maps with control on the degree distribution of black and white vertices. Our approach builds on the blossoming-tree paradigm, introducing a family of orientations on bipartite maps that extends Eulerian and quasi-Eulerian orientations and connects the bijection of Bousquet-M\'elou and Schaeffer to the general scheme of Albenque and Poulalhon. This enables us to generalize the Bousquet-M\'elou and Schaeffer's bijection to several families of bipartite maps. - As an application, we also derive a rational and Lagrangian parametrization with positive integer coefficients for the generating series of quartic maps equipped with an Ising model, which is key to the probabilistic study of these maps. - oai:arXiv.org:2511.03680v1 - math.CO - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Marie Albenque, Laurent M\'enard, Nicolas Tokka - - - Ising model with external magnetic field on random planar maps: Critical exponents - https://arxiv.org/abs/2511.03688 - arXiv:2511.03688v1 Announce Type: new -Abstract: We study the Ising model with an external magnetic field on random tetravalent planar maps and investigate its critical behavior. Explicit expressions for spontaneous magnetization and the susceptibility are computed and the critical exponents $\alpha=-1$ (third order phase transition), $\beta=\frac{1}{2}$ (spontaneous magnetization), $\gamma=2$ (susceptibility at zero external magnetic field) and $\delta=5$ (magnetization at critical temperature) are derived. To do so, we study the asymptotic behavior of the partition function of the model in the case of a weak external magnetic field using analytic combinatorics. - oai:arXiv.org:2511.03688v1 - math.PR - math-ph - math.CO - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Nicolas Tokka - - - A non-iterative straightening algorithm and orthogonality for skew Schur modules - https://arxiv.org/abs/2511.03702 - arXiv:2511.03702v1 Announce Type: new -Abstract: We generalize Fulton's determinantal construction of Schur modules to the skew setting, providing an explicit and functorial presentation using only elementary linear algebra and determinantal identities, in parallel with the partition case. Building on the non-iterative straightening formula of the first author for partition shapes, we develop a non-iterative straightening algorithm for skew Schur modules that expresses arbitrary elements in a new D-basis with an explicit closed coefficient formula. We then show that this D-basis is the result of applying Gram-Schmidt orthogonalization to the semistandard tableau basis, which identifies a natural inner product on the skew Schur module and recasts straightening as an orthogonal projection. - oai:arXiv.org:2511.03702v1 - math.CO - math.RT - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Reuven Hodges, Hanzhang Yin - - - Long-Lasting and Slowly Varying Transient Dynamics in Discrete-Time Systems - https://arxiv.org/abs/2511.03704 - arXiv:2511.03704v1 Announce Type: new -Abstract: Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics remain in a slowly evolving state for an extended period before undergoing rapid change. In this work, we analyze long-lasting and slowly varying transient dynamics in discrete-time systems based on extensions of previous theoretical frameworks developed for continuous-time systems. This involves clarifying the conditions under which we say an observable of the system exhibits prolonged transients, and deriving criteria for characterizing these dynamics. Our results show that specific points in the state space, analogous to previously defined transient centers in continuous-time systems, can generate and sustain long transients in discrete-time models. We demonstrate how these properties manifest in predator-prey models and epidemiological systems, particularly when populations or disease prevalence remain low for extended intervals before sudden shifts. - oai:arXiv.org:2511.03704v1 - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Anthony Pasion, Felicia Magpantay - - - The Adaptivity Barrier in Batched Nonparametric Bandits: Sharp Characterization of the Price of Unknown Margin - https://arxiv.org/abs/2511.03708 - arXiv:2511.03708v1 Announce Type: new -Abstract: We study batched nonparametric contextual bandits under a margin condition when the margin parameter $\alpha$ is unknown. To capture the statistical price of this ignorance, we introduce the regret inflation criterion, defined as the ratio between the regret of an adaptive algorithm and that of an oracle knowing $\alpha$. We show that the optimal regret inflation grows polynomial with the horizon $T$, with exponent precisely given by the value of a convex optimization problem involving the dimension, smoothness, and batch budget. Moreover, the minimizers of this optimization problem directly prescribe the batch allocation and exploration strategy of a rate-optimal algorithm. Building on this principle, we develop RoBIN (RObust batched algorithm with adaptive BINning), which achieves the optimal regret inflation up to logarithmic factors. These results reveal a new adaptivity barrier: under batching, adaptation to an unknown margin parameter inevitably incurs a polynomial penalty, sharply characterized by a variational problem. Remarkably, this barrier vanishes when the number of batches exceeds $\log \log T$; with only a doubly logarithmic number of updates, one can recover the oracle regret rate up to polylogarithmic factors. - oai:arXiv.org:2511.03708v1 - math.ST - cs.LG - stat.ML - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Rong Jiang, Cong Ma - - - A local Lorentzian Ferrand-Obata theorem for conformal vector fields - https://arxiv.org/abs/2511.03713 - arXiv:2511.03713v1 Announce Type: new -Abstract: For a conformal vector field on a closed, real-analytic, Lorentzian manifold we prove that the flow is locally isometric -- that it preserves a metric in the conformal class on a neighborhood of any point -- or the metric is everywhere conformally flat. The main theorem can be viewed as a local version of the Lorentzian Lichnerowicz conjecture in the real-analytic setting. The key result is an optimal improvement of the local normal forms for conformal vector fields of [FM13], which focused on non-linearizable singularities. This article is primarily concerned with essential linearizable singularities, and the proofs include global arguments which rely on the compactness assumption. - oai:arXiv.org:2511.03713v1 - math.DG - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Sorin Dumitrescu, Charles Frances, Karin Melnick, Vincent Pecastaing, Abdelghani Zeghib - - - Quantum Noise-Aware RIS-Aided Wireless Networks Using Variational Encoding and Signal Stabilization - https://arxiv.org/abs/2511.03717 - arXiv:2511.03717v1 Announce Type: new -Abstract: This paper presents a noise-aware quantum-assisted framework for blockage prediction in reconfigurable intelligent surface (RIS)-enabled wireless networks. The proposed architecture integrates a Quantum Base Station (QBS), a Quantum RIS (QRIS), and a mobile Quantum User Node (QUN). Visual information captured by an onboard RGB camera is amplitude-encoded into quantum states, while channel state observations are mapped into quantum rotation-encoded features. These hybrid inputs are processed through variational quantum circuits, enabling ternary classification of the link status. To address the inherent imperfections of noisy intermediate-scale quantum (NISQ) hardware, the system explicitly models depolarizing and dephasing channels along direct and QRIS-assisted paths. A fidelity-aware training objective is employed to jointly minimize classification loss and quantum state degradation, with amplitude damping and synthetic noise injection enhancing robustness. Simulation results on a quantum-adapted version of the ViWi dataset demonstrate that the proposed hybrid quantum model achieves superior accuracy and stability under realistic noise conditions, outperforming baseline and single-modality approaches. - oai:arXiv.org:2511.03717v1 - math.QA - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Shakil Ahmed - - - Distance Exceptional Graphs and the Curvature Index - https://arxiv.org/abs/2511.03719 - arXiv:2511.03719v1 Announce Type: new -Abstract: A graph $G=(V,E)$ on $n$ vertices is said to be \emph{distance exceptional} if the equation $D\vec{x} = \vec{1}$ admits no solution $\vec{x}\in\mathbb{R}^{n}$, where $D\in\mathbb{R}^{n\times n}$ is the shortest path distance matrix of $G$. These graphs were first studied by Steinerberger in the context of a notion of discrete curvature (``Curvature on graphs via equilibrium measures,'' \emph{Journal of Graph Theory}, 103(3), 2023). This work has led to several open questions about distance exceptional graphs, including: What is the structure of such graphs? How can they be characterized? How rare are they? In this paper, we investigate these questions through the lens of a graph invariant we term the \emph{curvature index}. We show that a graph is distance exceptional if and only if this invariant vanishes, and we develop a calculus for this invariant under graph operations including the Cartesian product and graph join. As a result, we recover and generalize a number of known results in this area. We show that any graph $G$ can be realized as an induced subgraph of a distance exceptional graph $G'$. Moreover, in many cases, this embedding is an isometry. In turn, this leads to a number of methods for constructing distance exceptional graphs. - oai:arXiv.org:2511.03719v1 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Sawyer Jack Robertson, Finn Southerland, Erlang Surya - - - Uncountably many homogeneous real trees with the same valence - https://arxiv.org/abs/2511.03722 - arXiv:2511.03722v1 Announce Type: new -Abstract: For any cardinal $\kappa \geq 2$, there is a unique complete real tree whose points all have valence $\kappa$. In this note, we show that, when $\kappa \geq 3$, it is necessary to assume completeness. More precisely, we show that there exist uncountably many homogeneous incomplete real trees whose points all have valence $\kappa$. - oai:arXiv.org:2511.03722v1 - math.MG - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - P\'en\'elope Azuelos - - - High-order Accumulative Regularization for Gradient Minimization in Convex Programming - https://arxiv.org/abs/2511.03723 - arXiv:2511.03723v1 Announce Type: new -Abstract: This paper develops a unified framework of high-order accumulative regularization (AR) framework for convex and uniformly convex gradient norm minimization. Existing high-order methods often exhibit a gap: the function value residual decreases fast, while the gradient norm converges much slower. To close this gap, we introduce AR that systematically transforms fast function value residual convergence rate into fast (matching) gradient norm convergence rate. - Specifically, for composite convex problems, for computing an approximate solution such that the norm of its (sub)gradient does not exceed $\varepsilon,$ the proposed AR methods match the best corresponding convergence rate for the function value residual. We further extend the framework to uniformly convex settings, establishing linear, superlinear and sublinear convergence of the gradient norm under different lower curvature conditions. Moreover, we design parameter-free algorithms that require no input of problem parameters, e.g., Lipschitz constant of the $p$-th order gradient, the initial optimality gap and the uniform convexity parameter, and allows inexact solution for each high-order step. To our best knowledge, no parameter-free methods can attain such a fast gradient norm convergence rate which matches that of the function value residual in the convex case, and no such parameter-free methods for uniformly convex problems exist. These results substantially generalize existing parameter-free and inexact high-order methods and recover first-order algorithms as special cases, providing a unified approach for fast gradient minimization across a broad range of smoothness and curvature regimes. - oai:arXiv.org:2511.03723v1 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yao Ji, Guanghui Lan - - - Mathematical exploration and discovery at scale - https://arxiv.org/abs/2511.02864 - arXiv:2511.02864v1 Announce Type: cross -Abstract: AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. - To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. - These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time. - oai:arXiv.org:2511.02864v1 - cs.NE - cs.AI - math.CA - math.CO - math.MG - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Bogdan Georgiev, Javier G\'omez-Serrano, Terence Tao, Adam Zsolt Wagner - - - Power Constrained Nonstationary Bandits with Habituation and Recovery Dynamics - https://arxiv.org/abs/2511.02944 - arXiv:2511.02944v1 Announce Type: cross -Abstract: A common challenge for decision makers is selecting actions whose rewards are unknown and evolve over time based on prior policies. For instance, repeated use may reduce an action's effectiveness (habituation), while inactivity may restore it (recovery). These nonstationarities are captured by the Reducing or Gaining Unknown Efficacy (ROGUE) bandit framework, which models real-world settings such as behavioral health interventions. While existing algorithms can compute sublinear regret policies to optimize these settings, they may not provide sufficient exploration due to overemphasis on exploitation, limiting the ability to estimate population-level effects. This is a challenge of particular interest in micro-randomized trials (MRTs) that aid researchers in developing just-in-time adaptive interventions that have population-level effects while still providing personalized recommendations to individuals. In this paper, we first develop ROGUE-TS, a Thompson Sampling algorithm tailored to the ROGUE framework, and provide theoretical guarantees of sublinear regret. We then introduce a probability clipping procedure to balance personalization and population-level learning, with quantified trade-off that balances regret and minimum exploration probability. Validation on two MRT datasets concerning physical activity promotion and bipolar disorder treatment shows that our methods both achieve lower regret than existing approaches and maintain high statistical power through the clipping procedure without significantly increasing regret. This enables reliable detection of treatment effects while accounting for individual behavioral dynamics. For researchers designing MRTs, our framework offers practical guidance on balancing personalization with statistical validity. - oai:arXiv.org:2511.02944v1 - cs.LG - cs.AI - math.OC - stat.ML - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fengxu Li, Stephanie M. Carpenter, Matthew P. Buman, Yonatan Mintz - - - Unifying Information-Theoretic and Pair-Counting Clustering Similarity - https://arxiv.org/abs/2511.03000 - arXiv:2511.03000v1 Announce Type: cross -Abstract: Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into two principal families, pair-counting and information-theoretic, reflecting whether they quantify agreement through element pairs or aggregate information across full cluster contingency tables. Prior work has uncovered parallels between these families and applied empirical normalization or chance-correction schemes, but their deeper analytical connection remains only partially understood. Here, we develop an analytical framework that unifies these families through two complementary perspectives. First, both families are expressed as weighted expansions of observed versus expected co-occurrences, with pair-counting arising as a quadratic, low-order approximation and information-theoretic measures as higher-order, frequency-weighted extensions. Second, we generalize pair-counting to $k$-tuple agreement and show that information-theoretic measures can be viewed as systematically accumulating higher-order co-assignment structure beyond the pairwise level. We illustrate the approaches analytically for the Rand index and Mutual Information, and show how other indices in each family emerge as natural extensions. Together, these views clarify when and why the two regimes diverge, relating their sensitivities directly to weighting and approximation order, and provide a principled basis for selecting, interpreting, and extending clustering similarity measures across applications. - oai:arXiv.org:2511.03000v1 - stat.ML - cs.IT - cs.LG - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Alexander J. Gates - - - Robust reduced-order model predictive control using peak-to-peak analysis of filtered signals - https://arxiv.org/abs/2511.03002 - arXiv:2511.03002v1 Announce Type: cross -Abstract: We address the design of a model predictive control (MPC) scheme for large-scale linear systems using reduced-order models (ROMs). Our approach uses a ROM, leverages tools from robust control, and integrates them into an MPC framework to achieve computational tractability with robust constraint satisfaction. Our key contribution is a method to obtain guaranteed bounds on the predicted outputs of the full-order system by predicting a (scalar) error-bounding system alongside the ROM. This bound is then used to formulate a robust ROM-based MPC that guarantees constraint satisfaction and robust performance. Our method is developed step-by-step by (i) analysing the error, (ii) bounding the peak-to-peak gain, an (iii) using filtered signals. We demonstrate our method on a 100-dimensional mass-spring-damper system, achieving over four orders of magnitude reduction in conservatism relative to existing approaches. - oai:arXiv.org:2511.03002v1 - eess.SY - cs.SY - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Johannes K\"ohler, Carlo Scholz, Melanie Zeilinger - - - Precise asymptotic analysis of Sobolev training for random feature models - https://arxiv.org/abs/2511.03050 - arXiv:2511.03050v1 Announce Type: cross -Abstract: Gradient information is widely useful and available in applications, and is therefore natural to include in the training of neural networks. Yet little is known theoretically about the impact of Sobolev training -- regression with both function and gradient data -- on the generalization error of highly overparameterized predictive models in high dimensions. In this paper, we obtain a precise characterization of this training modality for random feature (RF) models in the limit where the number of trainable parameters, input dimensions, and training data tend proportionally to infinity. Our model for Sobolev training reflects practical implementations by sketching gradient data onto finite dimensional subspaces. By combining the replica method from statistical physics with linearizations in operator-valued free probability theory, we derive a closed-form description for the generalization errors of the trained RF models. For target functions described by single-index models, we demonstrate that supplementing function data with additional gradient data does not universally improve predictive performance. Rather, the degree of overparameterization should inform the choice of training method. More broadly, our results identify settings where models perform optimally by interpolating noisy function and gradient data. - oai:arXiv.org:2511.03050v1 - stat.ML - cond-mat.dis-nn - cs.LG - math.PR - math.ST - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Katharine E Fisher, Matthew TC Li, Youssef Marzouk, Timo Schorlepp - - - Microgrids optimal radial reconfiguration via FORWARD algorithm - https://arxiv.org/abs/2511.03059 - arXiv:2511.03059v1 Announce Type: cross -Abstract: Microgrids offer a promising paradigm for integrating distributed energy resources, bolstering energy resilience, and reducing the impact of blackouts. However, their inherent decentralization and dynamic operation present substantial energy management complexities. These complexities, including balancing supply and demand, ensuring system stability, and minimizing operational costs, often necessitate solving computationally intractable NP-hard Mixed-Integer Non-Linear Programming (MINLP) problems. Traditional MINLP solvers struggle with the scalability and feasibility guarantees required for these challenges. To address this, this paper tackles the problem of resource allocation and radial configuration design for microgrid power distribution and proposes and abstracted problem which is solved by introducing a permutation-based iterative search method over the recently introduced FORWARD method to efficiently identify feasible, near-optimal radial network structures while inherently respecting physical constraints. Furthermore, this paper investigates the integration of the proposed method as a warm-start strategy for benchmark MINLP solvers offering a scalable solution for comprehensive microgrid design. - oai:arXiv.org:2511.03059v1 - eess.SY - cs.NA - cs.SY - math.NA - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Joan Vendrell Gallart, Russell Bent, Solmaz Kia - - - The Curved Spacetime of Transformer Architectures - https://arxiv.org/abs/2511.03060 - arXiv:2511.03060v1 Announce Type: cross -Abstract: We present a geometric framework for understanding Transformer-based language models, drawing an explicit analogy to General Relativity. Queries and keys induce an effective metric on representation space, and attention acts as a discrete connection that implements parallel transport of value vectors across tokens. Stacked layers provide discrete time-slices through which token representations evolve on this curved manifold, while backpropagation plays the role of a least-action principle that shapes loss-minimizing trajectories in parameter space. If this analogy is correct, token embeddings should not traverse straight paths in feature space; instead, their layer-wise steps should bend and reorient as interactions mediated by embedding space curvature. To test this prediction, we design experiments that expose both the presence and the consequences of curvature: (i) we visualize a curvature landscape for a full paragraph, revealing how local turning angles vary across tokens and layers; (ii) we show through simulations that excess counts of sharp/flat angles and longer length-to-chord ratios are not explainable by dimensionality or chance; and (iii) inspired by Einstein's eclipse experiment, we probe deflection under controlled context edits, demonstrating measurable, meaning-consistent bends in embedding trajectories that confirm attention-induced curvature. - oai:arXiv.org:2511.03060v1 - cs.LG - cs.CL - math.DG - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Riccardo Di Sipio, Jairo Diaz-Rodriguez, Luis Serrano - - - Beyond Maximum Likelihood: Variational Inequality Estimation for Generalized Linear Models - https://arxiv.org/abs/2511.03087 - arXiv:2511.03087v1 Announce Type: cross -Abstract: Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical method for parameter inference. While MLE performs well in canonical GLMs, it can become computationally inefficient near the true parameter value. In more general settings with non-canonical or fully general link functions, the resulting optimization landscape is often non-convex, non-smooth, and numerically unstable. To address these challenges, we investigate an alternative estimator based on solving the variational inequality (VI) formulation of the GLM likelihood equations, originally proposed by Juditsky and Nemirovski as an alternative for solving nonlinear least-squares problems. Unlike their focus on algorithmic convergence in monotone settings, we analyze the VI approach from a statistical perspective, comparing it systematically with the MLE. We also extend the theory of VI estimators to a broader class of link functions, including non-monotone cases satisfying a strong Minty condition, and show that it admits weaker smoothness requirements than MLE, enabling faster, more stable, and less locally trapped optimization. Theoretically, we establish both non-asymptotic estimation error bounds and asymptotic normality for the VI estimator, and further provide convergence guarantees for fixed-point and stochastic approximation algorithms. Numerical experiments show that the VI framework preserves the statistical efficiency of MLE while substantially extending its applicability to more challenging GLM settings. - oai:arXiv.org:2511.03087v1 - stat.ME - math.OC - math.ST - stat.ML - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Linglingzhi Zhu, Jonghyeok Lee, Yao Xie - - - A Plug-and-Play Framework for Volumetric Light-Sheet Image Reconstruction - https://arxiv.org/abs/2511.03093 - arXiv:2511.03093v1 Announce Type: cross -Abstract: Cardiac contraction is a rapid, coordinated process that unfolds across three-dimensional tissue on millisecond timescales. Traditional optical imaging is often inadequate for capturing dynamic cellular structure in the beating heart because of a fundamental trade-off between spatial and temporal resolution. To overcome these limitations, we propose a high-performance computational imaging framework that integrates Compressive Sensing (CS) with Light-Sheet Microscopy (LSM) for efficient, low-phototoxic cardiac imaging. The system performs compressed acquisition of fluorescence signals via random binary mask coding using a Digital Micromirror Device (DMD). We propose a Plug-and-Play (PnP) framework, solved using the alternating direction method of multipliers (ADMM), which flexibly incorporates advanced denoisers, including Tikhonov, Total Variation (TV), and BM3D. To preserve structural continuity in dynamic imaging, we further introduce temporal regularization enforcing smoothness between adjacent z-slices. Experimental results on zebrafish heart imaging under high compression ratios demonstrate that the proposed method successfully reconstructs cellular structures with excellent denoising performance and image clarity, validating the effectiveness and robustness of our algorithm in real-world high-speed, low-light biological imaging scenarios. - oai:arXiv.org:2511.03093v1 - cs.CV - cs.NA - math.NA - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Yi Gong, Xinyuan Zhang, Jichen Chai, Yichen Ding, Yifei Lou - - - An Efficient Classification Model for Cyber Text - https://arxiv.org/abs/2511.03107 - arXiv:2511.03107v1 Announce Type: cross -Abstract: The uprising of deep learning methodology and practice in recent years has brought about a severe consequence of increasing carbon footprint due to the insatiable demand for computational resources and power. The field of text analytics also experienced a massive transformation in this trend of monopolizing methodology. In this paper, the original TF-IDF algorithm has been modified, and Clement Term Frequency-Inverse Document Frequency (CTF-IDF) has been proposed for data preprocessing. This paper primarily discusses the effectiveness of classical machine learning techniques in text analytics with CTF-IDF and a faster IRLBA algorithm for dimensionality reduction. The introduction of both of these techniques in the conventional text analytics pipeline ensures a more efficient, faster, and less computationally intensive application when compared with deep learning methodology regarding carbon footprint, with minor compromise in accuracy. The experimental results also exhibit a manifold of reduction in time complexity and improvement of model accuracy for the classical machine learning methods discussed further in this paper. - oai:arXiv.org:2511.03107v1 - cs.LG - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Md Sakhawat Hossen, Md. Zashid Iqbal Borshon, A. S. M. Badrudduza - - - Exact solutions of the reverse space-time higher-order modified self-steepening nonlinear Schr\"odinger equation - https://arxiv.org/abs/2511.03118 - arXiv:2511.03118v1 Announce Type: cross -Abstract: This paper investigates a reverse space-time higher-order modified self-steepening nonlinear Schr\"odinger equation, which distinguishes its standard local counterparts through the reverse space-time symmetry. The integrability of this nonlocal equation is rigorously verified by presenting its associated Lax pair and infinitely many conservation laws. Utilizing the Darboux transformation, we systematically construct a diverse range of localized wave solutions on both zero and nonzero backgrounds. These patterns, such as kinks, exponentially decaying solitons, asymmetric rogue waves and their interaction solutions, exhibit novel dynamical behaviors that are not found in the local counterparts. This work not only enriches the family of solutions for the equation, but also highlights the effectiveness of the Darboux transformation in exploring nonlinear wave dynamics in nonlocal systems. - oai:arXiv.org:2511.03118v1 - nlin.SI - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yanan Wang, Xi-hu Wu - - - Commutative Algebra Modeling in Materials Science -- A Case Study on Metal-Organic Frameworks (MOFs) - https://arxiv.org/abs/2511.03124 - arXiv:2511.03124v1 Announce Type: cross -Abstract: Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract algebra that has been rarely applied in data and material sciences. We introduce the first ever commutative algebra modeling and prediction in materials science. Specifically, category-specific commutative algebra (CSCA) is proposed as a new framework for MOF representation and learning. It integrates element-based categorization with multiscale algebraic invariants to encode both local coordination motifs and global network organization of MOFs. These algebraically consistent, chemically aware representations enable compact, interpretable, and data efficient modeling of MOF properties such as Henry's constants and uptake capacities for common gases. Compared to traditional geometric and graph-based approaches, CSCA achieves comparable or superior predictive accuracy while substantially improving interpretability and stability across data sets. By aligning commutative algebra with the chemical hierarchy, the CSCA establishes a rigorous and generalizable paradigm for understanding structure and property relationships in porous materials and provides a nonlinear algebra-based framework for data-driven material discovery. - oai:arXiv.org:2511.03124v1 - cond-mat.mtrl-sci - math.AC - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Caleb Simiyu Khaemba, Hongsong Feng, Dong Chen, Chun-Long Chen, Guo-Wei Wei - - - A Theory of Saving under Risk Preference Dynamics - https://arxiv.org/abs/2511.03142 - arXiv:2511.03142v1 Announce Type: cross -Abstract: Empirical evidence shows that wealthy households have substantially higher saving rates and markedly lower marginal propensity to consume (MPC) than other groups. Existing theory can account for this pattern only under restrictive assumptions on returns, discounting, and preferences. This paper develops a general theory of optimal savings with preference shocks, allowing risk aversion to vary across states and over time. We show that incorporating such heterogeneity in risk attitudes fundamentally alters the asymptotic dynamics of consumption and saving. In particular, we provide an analytical characterization of the asymptotic MPCs and show that zero asymptotic MPCs, corresponding to a 100\% asymptotic saving rate, arise under markedly weaker conditions than in existing theory. Strikingly, such outcomes occur whenever there is a positive probability that agents become less risk averse in the future. As a result, the vanishing MPC emerges as a generic feature rather than a knife-edge result of the optimal savings model, offering a more theoretically robust and empirically consistent account of the saving behavior of wealthy households. - oai:arXiv.org:2511.03142v1 - econ.TH - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Qingyin Ma, Xinxi Song, Alexis Akira Toda - - - Balanced contributions, consistency, and value for games with externalities - https://arxiv.org/abs/2511.03145 - arXiv:2511.03145v1 Announce Type: cross -Abstract: We consider fair and consistent extensions of the Shapley value for games with externalities. Based on the restriction identified by Casajus et al. (2024, Games Econ. Behavior 147, 88-146), we define balanced contributions, Sobolev's consistency, and Hart and Mas-Colell's consistency for games with externalities, and we show that these properties lead to characterizations of the generalization of the Shapley value introduced by Macho-Stadler et al. (2007, J. Econ. Theory 135, 339-356), that parallel important characterizations of the Shapley value. - oai:arXiv.org:2511.03145v1 - econ.TH - cs.GT - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-sa/4.0/ - Andr\'e Casajus, Yukihiko Funaki, Frank Huettner - - - Decoupled Entropy Minimization - https://arxiv.org/abs/2511.03256 - arXiv:2511.03256v1 Announce Type: cross -Abstract: Entropy Minimization (EM) is beneficial to reducing class overlap, bridging domain gap, and restricting uncertainty for various tasks in machine learning, yet its potential is limited. To study the internal mechanism of EM, we reformulate and decouple the classical EM into two parts with opposite effects: cluster aggregation driving factor (CADF) rewards dominant classes and prompts a peaked output distribution, while gradient mitigation calibrator (GMC) penalizes high-confidence classes based on predicted probabilities. Furthermore, we reveal the limitations of classical EM caused by its coupled formulation: 1) reward collapse impedes the contribution of high-certainty samples in the learning process, and 2) easy-class bias induces misalignment between output distribution and label distribution. To address these issues, we propose Adaptive Decoupled Entropy Minimization (AdaDEM), which normalizes the reward brought from CADF and employs a marginal entropy calibrator (MEC) to replace GMC. AdaDEM outperforms DEM*, an upper-bound variant of classical EM, and achieves superior performance across various imperfectly supervised learning tasks in noisy and dynamic environments. - oai:arXiv.org:2511.03256v1 - cs.LG - cs.CV - cs.IT - math.IT - math.ST - stat.ML - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jing Ma, Hanlin Li, Xiang Xiang - - - Evolutionary Dynamics in Continuous-time Finite-state Mean Field Games - Part II: Stability - https://arxiv.org/abs/2511.03297 - arXiv:2511.03297v1 Announce Type: cross -Abstract: We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends not only on their own state and action but also on the distribution of states and actions across the population, capturing effects such as congestion in traffic networks. In Part I, we introduced an evolutionary model and a new solution concept - the mixed stationary Nash Equilibrium (MSNE) - which coincides with the rest points of the mean field evolutionary model under meaningful families of revision protocols. In this second part, we investigate the evolutionary stability of MSNE. We derive conditions on both the structure of the MSNE and the game's payoff map that ensure local and global stability under evolutionary dynamics. These results characterize when MSNE can robustly emerge and persist against strategic deviations, thereby providing insight into its long-term viability in large population dynamic games. - oai:arXiv.org:2511.03297v1 - eess.SY - cs.GT - cs.SY - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Leonardo Pedroso, Andrea Agazzi, W. P. M. H. Heemels, Mauro Salazar - - - Symmetry-induced activity patterns of active-inactive clusters in complex networks - https://arxiv.org/abs/2511.03300 - arXiv:2511.03300v1 Announce Type: cross -Abstract: We present activity patterns consisting of active and inactive clusters of synchronized nodes in networks. We call a cluster active if nodes in it have nonzero velocity and inactive vice versa. The simultaneous invariance of active and inactive clusters poses a challenge because fluctuations from active clusters must cancel out for a desired cluster to be inactive. With the help of permutation symmetries in network topology and selecting dynamics on top such that internal dynamics and coupling functions are odd functions in the phase space, we demonstrate that such a combination of structure and dynamics exhibits (stable) invariant patterns consisting of active and inactive clusters. Symmetry breaking of synchronized clusters creates active clusters that are in antisynchrony with each other, resulting in the cancellation of fluctuations for clusters connected with these antisynchronous clusters. Furthermore, as the coupling between nodes changes, active clusters lose their activity at different coupling values, and the network transitions from one activity pattern to another. Numerical simulations have been presented for networks of Van der Pol and Stuart-Landau oscillators. We extend the master stability approach to these patterns and provide stability conditions for their existence. - oai:arXiv.org:2511.03300v1 - nlin.AO - math.DS - nlin.PS - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Anil Kumar, V. K. Chandrasekar, D. V. Senthilkumar - - - Heat Kernels and Resummations: the Spinor Case - https://arxiv.org/abs/2511.03315 - arXiv:2511.03315v1 Announce Type: cross -Abstract: Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation patterns within the heat kernel expansion are examined as a means of systematically extracting nonperturbative information. Building upon previous results for Yukawa interactions and scalar quantum electrodynamics, we extend the analysis to spinor fields, demonstrating that a recently conjectured resummation structure continues to hold. The resulting formulation yields a compact expression that resums invariants constructed from the electromagnetic tensor and its spinorial couplings, while preserving agreement with known proper-time coefficients. Beyond its immediate computational utility, the framework offers a unified perspective on the emergence of nonperturbative effects (such as Schwinger pair creation) in relation to perturbative heat kernel data, and provides a basis for future extensions to curved spacetimes and non-Abelian gauge theories. - oai:arXiv.org:2511.03315v1 - hep-th - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - S. A. Franchino-Vi\~nas, C. Garc\'ia-P\'erez, F. D. Mazzitelli, S. Pla, V. Vitagliano - - - Two thousand years of the oracle problem. Insights from Ancient Delphi on the future of blockchain oracles - https://arxiv.org/abs/2511.03319 - arXiv:2511.03319v1 Announce Type: cross -Abstract: The oracle problem refers to the inability of an agent to know if the information coming from an oracle is authentic and unbiased. In ancient times, philosophers and historians debated on how to evaluate, increase, and secure the reliability of oracle predictions, particularly those from Delphi, which pertained to matters of state. Today, we refer to data carriers for automatic machines as oracles, but establishing a secure channel between these oracles and the real world still represents a challenge. Despite numerous efforts, this problem remains mostly unsolved, and the recent advent of blockchain oracles has added a layer of complexity because of the decentralization of blockchains. This paper conceptually connects Delphic and modern blockchain oracles, developing a comparative framework. Leveraging blockchain oracle taxonomy, lexical analysis is also performed on 167 Delphic queries to shed light on the relationship between oracle answer quality and question type. The presented framework aims first at revealing commonalities between classical and computational oracles and then at enriching the oracle analysis within each field. This study contributes to the computer science literature by proposing strategies to improve the reliability of blockchain oracles based on insights from Delphi and to classical literature by introducing a framework that can also be applied to interpret and classify other ancient oracular mechanisms. - oai:arXiv.org:2511.03319v1 - cs.CR - cs.CY - cs.IR - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Giulio Caldarelli, Massimiliano Ornaghi - - - Branch-and-Cut for Computing Approximate Equilibria of Mixed-Integer Generalized Nash Games - https://arxiv.org/abs/2511.03340 - arXiv:2511.03340v1 Announce Type: cross -Abstract: Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by the rivals' strategies. However, such games are known for failing to admit exact equilibria and also the assumption of all players being able to solve nonconvex problems to global optimality is questionable. This motivates the study of approximate equilibria. In this work, we consider an approximation concept that incorporates both multiplicative and additive relaxations of optimality. We propose a branch-and-cut (B&C) method that computes such approximate equilibria or proves its non-existence. For this, we adopt the idea of intersection cuts and show the existence of such cuts under the condition that the constraints are linear and each player's cost function is either convex in the entire strategy profile, or, concave in the entire strategy profile and linear in the rivals' strategies. For the special case of standard Nash equilibrium problems, we introduce an alternative type of cut and show that the method terminates finitely, provided that each player has only finitely many distinct best-response sets. Finally, on the basis of the B&C method, we introduce a single-tree binary-search method to compute best-approximate equilibria under some simplifying assumptions. We implemented these methods and present numerical results for a class of mixed-integer flow games. - oai:arXiv.org:2511.03340v1 - cs.GT - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alo\"is Duguet, Tobias Harks, Martin Schmidt, Julian Schwarz - - - A superintegrable quantum field theory - https://arxiv.org/abs/2511.03373 - arXiv:2511.03373v1 Announce Type: cross -Abstract: G\'erard and Grellier proposed, under the name of the cubic Szeg\H{o} equation, a remarkable classical field theory on a circle with a quartic Hamiltonian. The Lax integrability structure that emerges from their definition is so constraining that it allows for writing down an explicit general solution for prescribed initial data, and at the same time, the dynamics is highly nontrivial and involves turbulent energy transfer to arbitrarily short wavelengths. The quantum version of the same Hamiltonian is even more striking: not only the Hamiltonian itself, but also its associated conserved hierarchies display purely integer spectra, indicating a structure beyond ordinary quantum integrability. Here, we initiate a systematic study of this quantum system by presenting a mixture of analytic results and empirical observations on the structure of its eigenvalues and eigenvectors, conservation laws, ladder operators, etc. - oai:arXiv.org:2511.03373v1 - nlin.SI - hep-th - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Marine De Clerck, Oleg Evnin - - - Hesse's Redemption: Efficient Convex Polynomial Programming - https://arxiv.org/abs/2511.03440 - arXiv:2511.03440v1 Announce Type: cross -Abstract: Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic programming, such solution bounds follow from classical characterizations of optimal solutions by systems of linear equations. For other programs, e.g., semidefinite ones, examples due to Khachiyan show that optimal solutions may require huge coefficients with an exponential number of bits, even if we allow approximations. Correspondingly, semidefinite programming is not even known to be in NP. The unconstrained minimization of convex polynomials of degree four and higher has remained a fundamental open problem between these two extremes: its optimal solutions do not admit a linear characterization and, at the same time, Khachiyan-type examples do not apply. We resolve this problem by developing new techniques to prove solution bounds when no linear characterizations are available. Even for programs minimizing a convex polynomial (of arbitrary degree) over a polyhedron, we prove that the existence of an optimal solution implies that an approximately optimal one with polynomial bit length also exists. These solution bounds, combined with the ellipsoid method, yield the first polynomial-time algorithm for convex polynomial programming, settling a question posed by Nesterov (Math. Program., 2019). Before, no polynomial-time algorithm was known even for unconstrained minimization of a convex polynomial of degree four. - oai:arXiv.org:2511.03440v1 - cs.DS - cs.CC - math.AG - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Lucas Slot, David Steurer, Manuel Wiedmer - - - The Converse Madelung Question - https://arxiv.org/abs/2511.03552 - arXiv:2511.03552v1 Announce Type: cross -Abstract: We pose the converse Madelung question: not whether Fisher information can reproduce quantum mechanics, but whether it is necessary. We work with minimal, physically motivated axioms on density and phase: locality, probability conservation, Euclidean invariance with a global phase symmetry, reversibility, and convex regularity. Within the resulting class of first order local Hamiltonian field theories, these axioms single out the canonical Poisson bracket on density and phase under the Dubrovin and Novikov assumptions for local hydrodynamic brackets. Using a pointwise, gauge covariant complex change of variables that maps density and phase to a single complex field, we show that the only convex, rotationally invariant, first derivative local functional of the density whose Euler Lagrange term yields a reversible completion that is exactly projectively linear is the Fisher functional. When its coefficient equals Planck constant squared divided by twice the mass, the dynamics reduce to the linear Schrodinger equation. For many body systems, a single local complex structure across sectors enforces the same relation species by species, fixing a single Planck constant. Galilean covariance appears through the Bargmann central extension, with the usual superselection consequences. Comparison with the Doebner and Goldin family identifies the reversible zero diffusion corner with linear Schrodinger dynamics. We provide operational falsifiers via residual diagnostics for the continuity and Hamilton Jacobi equations and report numerical minima at the Fisher scale that are invariant under Galilean boosts. In this setting, quantum mechanics emerges as a reversible fixed point of Fisher regularised information hydrodynamics. A code archive enables direct numerical checks, including a superposition stress test that preserves exact projective linearity within our axioms. - oai:arXiv.org:2511.03552v1 - quant-ph - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Jonathan R Dunkley - - - Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity - https://arxiv.org/abs/2511.03606 - arXiv:2511.03606v1 Announce Type: cross -Abstract: The study of self-normalized processes plays a crucial role in a wide range of applications, from sequential decision-making to econometrics. While the behavior of self-normalized concentration has been widely investigated for scalar-valued processes, vector-valued processes remain comparatively underexplored, especially outside of the sub-Gaussian framework. In this contribution, we provide concentration bounds for self-normalized processes with light tails beyond sub-Gaussianity (such as Bennett or Bernstein bounds). We illustrate the relevance of our results in the context of online linear regression, with applications in (kernelized) linear bandits. - oai:arXiv.org:2511.03606v1 - stat.ML - cs.LG - math.ST - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Diego Martinez-Taboada, Tomas Gonzalez, Aaditya Ramdas - - - Final state sensitivity and fractal basin boundaries from coupled Chialvo neurons - https://arxiv.org/abs/2511.03671 - arXiv:2511.03671v1 Announce Type: cross -Abstract: We investigate and quantify the basin geometry and extreme final state uncertainty of two identical electrically asymmetrically coupled Chialvo neurons. The system's diverse behaviors are presented, along with the mathematical reasoning behind its chaotic and nonchaotic dynamics as determined by the structure of the coupled equations. The system is found to be multistable with two qualitatively different attractors. Although each neuron is individually nonchaotic, the chaotic basin takes up the vast majority of the coupled system's state space, but the nonchaotic basin stretches to infinity due to chance synchronization. The boundary between the basins is found to be fractal, leading to extreme final state sensitivity. This uncertainty and its potential effect on the synchronization of biological neurons may have significant implications for understanding human behavior and neurological disease. - oai:arXiv.org:2511.03671v1 - nlin.CD - math.DS - physics.bio-ph - q-bio.NC - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Bennett Lamb, Brandon B. Le - - - Impact of Resistance Development Mechanisms on Antibiotic Treatment Outcomes - https://arxiv.org/abs/2511.03677 - arXiv:2511.03677v1 Announce Type: cross -Abstract: Bacteria develop resistance to antibiotics through various mechanisms, with the specific mechanism depending on the drug-bacteria pair. It remains unclear, however, which resistance mechanism best supports favorable treatment outcomes, specifically in clearing infections and inhibiting further resistance. In this study, we use periodic ordinary differential equation models to simulate different antibiotic treatment protocols for bacterial infections. Using stability analysis and numerical simulations, we investigate how different resistance mechanisms, including plasmid-induced and mutation-induced resistance, affect treatment outcomes. Our findings suggest that antibiotic treatments with fixed dosing schedules are more likely to be effective when resistance arises exclusively through plasmid-mediated transmission. Further, when treatment fails, mutation-driven mechanisms tend to favor the selection of fully resistant bacterial strains. We also investigated the efficacy of different treatment strategies based on these mechanisms, finding that a twice-daily regimen consistently outperforms a once-daily regimen in terms of infection clearance. Additionally, our simulations with short half-life antibiotics indicate that the "catch-up" strategy outperforms the "compensatory double-dose" approach after a missed dose, a finding that aligns with general pharmaceutical advice for short-half-life drugs. - oai:arXiv.org:2511.03677v1 - q-bio.PE - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ailin Zhang, Shigui Ruan, Xi Huo - - - Mean-field approach to finite-size fluctuations in the Kuramoto-Sakaguchi model - https://arxiv.org/abs/2511.03700 - arXiv:2511.03700v1 Announce Type: cross -Abstract: We develop an ab initio approach to describe the statistical behavior of finite-size fluctuations in the Kuramoto-Sakaguchi model. We obtain explicit expressions for the covariance function of fluctuations of the complex order parameter and determine the variance of its magnitude entirely in terms of the equation parameters. Our results rely on an explicit complex-valued formula for solutions of the Adler equation. We present analytical results for both the sub- and the super-critical case. Moreover, our framework does not require any prior knowledge about the structure of the partially synchronized state. We corroborate our results with numerical simulations of the full Kuramoto-Sakaguchi model. The proposed methodology is sufficiently general such that it can be applied to other interacting particle systems. - oai:arXiv.org:2511.03700v1 - nlin.AO - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Oleh E. Omel'chenko, Georg A. Gottwald - - - Median geometry for spaces with measured walls and for groups - https://arxiv.org/abs/1708.00254 - arXiv:1708.00254v4 Announce Type: replace -Abstract: We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of compatibility possible with the median geometry. Our theorem is also relevant for potential Rips-type theorems for median spaces. The result follows from an analysis of a quasification of median geometry that provides a geometric characterization of spaces at finite Hausdorff distance from a median space. We explain how the case of complex hyperbolic metric spaces is different, and that such spaces cannot be at finite Hausdorff distance from a median space. - oai:arXiv.org:1708.00254v4 - math.GT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1007/s00208-025-03289-1 - Indira Chatterji, Cornelia Dru\c{t}u - - - Volterra type integral operator and analytic function spaces - https://arxiv.org/abs/1805.01043 - arXiv:1805.01043v3 Announce Type: replace -Abstract: We investigate the geometric properties of the Volterra-type integral operator \begin{equation*} T_g[f](z) = \int_{0}^{z} f(s)\, g'(s)\, ds, \quad |z|<1, \end{equation*} acting on various subclasses of analytic functions in the unit disk. Sharp estimates are obtained for the convexity radius of $T_g$, which simultaneously determine its univalence radius, across several classical function families. In addition, we introduce and study higher-order Volterra-type operators, establish their normalized forms, and propose an open question on the scaling behavior of their convexity radii. - oai:arXiv.org:1805.01043v3 - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Rahim Kargar - - - Fukaya A_\infty-structures associated to Lefschetz fibrations. VI - https://arxiv.org/abs/1810.07119 - arXiv:1810.07119v4 Announce Type: replace -Abstract: To a symplectic Lefschetz pencil on a monotone symplectic manifold, we associate an algebraic structure, which is a pencil of categories in the sense of noncommutative geometry. One fibre of this "noncommutative pencil" is related to the Fukaya category of the open (meaning, with the base locus removed, and hence exact symplectic) fibre of the original Lefschetz pencil; the other fibres are newly constructed kinds of Fukaya categories. - oai:arXiv.org:1810.07119v4 - math.SG - math.KT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Paul Seidel - - - Vector-valued Fourier hyperfunctions and boundary values - https://arxiv.org/abs/1912.03659 - arXiv:1912.03659v2 Announce Type: replace -Abstract: This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a complex non-necessarily metrisable locally convex Hausdorff space $E$. Moreover, necessary and sufficient conditions are described such that a reasonable theory of $E$-valued Fourier hyperfunctions exists. In particular, if $E$ is an ultrabornological PLS-space, such a theory is possible if and only if E satisfies the so-called property $(PA)$. Furthermore, many examples of such spaces having $(PA)$ resp. not having $(PA)$ are provided. We also prove that the vector-valued Fourier hyperfunctions can be realized as the sheaf generated by equivalence classes of certain compactly supported $E$-valued functionals and interpreted as boundary values of slowly increasing holomorphic functions. - oai:arXiv.org:1912.03659v2 - math.FA - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1215/21562261-2024-0030 - Kyoto Journal of Mathematics (2025, Online first), 1-65 - Karsten Kruse - - - Parallel computation of interval bases for persistence module decomposition - https://arxiv.org/abs/2106.11884 - arXiv:2106.11884v3 Announce Type: replace -Abstract: A persistence module $M$, with coefficients in a field $\mathbb{F}$, is a finite-dimensional linear representation of an equioriented quiver of type $A_n$ or, equivalently, a graded module over the ring of polynomials $\mathbb{F}[x]$. It is well-known that $M$ can be written as the direct sum of indecomposable representations or as the direct sum of cyclic submodules generated by homogeneous elements. An interval basis for $M$ is a set of homogeneous elements of $M$ such that the sum of the cyclic submodules of $M$ generated by them is direct and equal to $M$. We introduce a novel algorithm to compute an interval basis for $M$. Based on a flag of kernels of the structure maps, our algorithm is suitable for parallel or distributed computation and does not rely on a presentation of $M$. This algorithm outperforms the approach via the presentation matrix and Smith Normal Form. We specialize our parallel approach to persistent homology modules, and we close by applying the proposed algorithm to tracking harmonics via Hodge decomposition. - oai:arXiv.org:2106.11884v3 - math.AT - cs.CG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1007/s00200-025-00699-1 - A. De Gregorio, M. Guerra, S. Scaramuccia, F. Vaccarino, Parallel computation of interval bases for persistence module decomposition, Appl. Algebr. Eng. Commun. Comput. (2025) - Alessandro De Gregorio, Marco Guerra, Sara Scaramuccia, Francesco Vaccarino - - - On the definition of stable transfer factors - https://arxiv.org/abs/2203.03783 - arXiv:2203.03783v3 Announce Type: replace -Abstract: We construct stable geometric and spectral transfer factors for a general reductive group and develop some of their basic properties, assuming the refined local Langlands correspondence. Using our definition of stable geometric transfer factors, we show that the stable transfer conjecture for orbital integrals implies the stable transfer of characters and vice versa. The latter is also implied by local Langlands, and in particular this establishes archimedean stable geometric transfer. Finally, we show how the stable geometric transfer factors can be used to define stable spectral transfer factors. - oai:arXiv.org:2203.03783v3 - math.RT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tian An Wong - - - Symplectic polarity and Mahler's conjecture - https://arxiv.org/abs/2211.14630 - arXiv:2211.14630v3 Announce Type: replace -Abstract: We state a conjecture about the volume of symplectically self-polar convex bodies and show that it is equivalent to Mahler's conjecture concerning the volume of a convex body and its Euclidean polar. We also establish lower and upper bounds for symplectic capacities of symplectically self-polar bodies. - oai:arXiv.org:2211.14630v3 - math.MG - math.SG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mark Berezovik, Roman Karasev - - - Uniform-in-time propagation of chaos for mean field Langevin dynamics - https://arxiv.org/abs/2212.03050 - arXiv:2212.03050v4 Announce Type: replace -Abstract: We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the mean field dynamics. Furthermore, we prove the uniform-in-time propagation of chaos in both the $L^2$-Wasserstein metric and relative entropy. - oai:arXiv.org:2212.03050v4 - math.PR - stat.ML - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1214/24-AIHP1499 - Ann. Inst. Henri Poincar\'e, Probab. Stat., 61(4):2357-2404, 2025 - Fan Chen, Zhenjie Ren, Songbo Wang - - - How to construct decay rates for kinetic Fokker--Planck equations? - https://arxiv.org/abs/2302.14506 - arXiv:2302.14506v5 Announce Type: replace -Abstract: We study time averages for the norm of solutions to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimates for systems subject to a confining potential, allowing fat-tail, sub-exponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The key step in our estimates is a modified Poincar\'e inequality, obtained via a Lions--Poincar\'e inequality and an averaging lemma. - oai:arXiv.org:2302.14506v5 - math.AP - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Giovanni Brigati, Gabriel Stoltz - - - Matrix models for the nested hypergeometric tau-functions - https://arxiv.org/abs/2304.03051 - arXiv:2304.03051v3 Announce Type: replace -Abstract: We introduce and investigate a family of tau-functions of the 2D Toda hierarchy, which is a natural generalization of the hypergeometric family associated with Hurwitz numbers. For this family we prove a skew Schur function expansion formula. For arbitrary rational weight generating functions we construct the multi-matrix models. Two different types of cut-and-join descriptions are derived. Considered examples include generalized fully simple maps, which we identify with the recently introduced skew hypergeometric tau-functions. - oai:arXiv.org:2304.03051v3 - math-ph - hep-th - math.MP - nlin.SI - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - 10.4310/CNTP.250531024251 - Commun.Num.Theor.Phys. 19 (2025) 2, 241-288 - Alexander Alexandrov - - - Universal Proof Theory, TACL 2022 Lecture Notes - https://arxiv.org/abs/2305.10888 - arXiv:2305.10888v3 Announce Type: replace -Abstract: These lecture notes survey the emerging area of Universal Proof Theory, which investigates general questions about the existence, equivalence, and characterization of good proof systems for broad classes of logics. In particular, the notes concentrate on the existence problem: for which logics do there exist proof systems satisfying desirable meta-properties (e.g. cut elimination, analyticity, termination)? After a brief historical and conceptual introduction, we survey different flavours of proof theory (Hilbert systems, natural deduction, sequent calculi) in the context of classical, intuitionistic, modal, and substructural logics. We then develop a general method for obtaining positive and negative existence results, based on interpolation and uniform interpolation techniques, and apply it to a range of logics (intermediate, modal, non-normal, conditional, and substructural). We also discuss variations of the method. As these are lecture notes, proofs are often sketched or omitted, with pointers to papers containing the full proofs. The survey thus aims to chart the scope and challenges of Universal Proof Theory for future work. - oai:arXiv.org:2305.10888v3 - math.LO - cs.LO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Rosalie Iemhoff, Raheleh Jalali - - - The algebra of higher homotopy operations - https://arxiv.org/abs/2307.12017 - arXiv:2307.12017v2 Announce Type: replace -Abstract: We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure. - oai:arXiv.org:2307.12017v2 - math.AT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Samik Basu, David Blanc, Debasis Sen - - - The Kudla-Millson lift of Siegel cusp forms - https://arxiv.org/abs/2307.15809 - arXiv:2307.15809v2 Announce Type: replace -Abstract: We study the injectivity of the Kudla-Millson lift of genus 2 Siegel cusp forms, vector-valued with respect to the Weil representation associated to an even lattice L. We prove that if L splits off two hyperbolic planes and is of sufficiently large rank, then the lift is injective. As an application, we deduce that the image of the lift in the degree 4 cohomology of the associated orthogonal Shimura variety has the same dimension as the lifted space of cusp forms. Our results also cover the case of moduli spaces of quasi-polarized K3 surfaces. To prove the injectivity, we introduce vector-valued indefinite Siegel theta functions of genus 2 and of Jacobi type attached to L. We describe their behavior with respect to the split of a hyperbolic plane in L. This generalizes results of Borcherds to genus higher than 1. - oai:arXiv.org:2307.15809v2 - math.NT - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Paul Kiefer, Riccardo Zuffetti - - - On CAT($\kappa$) surfaces - https://arxiv.org/abs/2309.13533 - arXiv:2309.13533v3 Announce Type: replace -Abstract: We study the properties of $\text{CAT}(\kappa)$ surfaces: length metric spaces homeomorphic to a surface having curvature bounded above in the sense of satisfying the $\text{CAT}(\kappa)$ condition locally. The main facts about $\text{CAT}(\kappa)$ surfaces seem to be largely a part of mathematical folklore, and this paper is intended to rectify the situation. We provide a complete proof that $\text{CAT}(\kappa)$ surfaces have bounded (integral) curvature. This fact allows one to apply the established theory of surfaces of bounded curvature to derive further properties of $\text{CAT}(\kappa)$ surfaces. We also show that $\text{CAT}(\kappa)$ surfaces can be approximated by smooth Riemannian surfaces of Gaussian curvature at most $\kappa$. We do this by giving explicit formulas for smoothing the vertices of model polyhedral surfaces. - oai:arXiv.org:2309.13533v3 - math.MG - math.DG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Saajid Chowdhury, Hechen Hu, Matthew Romney, Adam Tsou - - - Spectral Moment Formulae for $\hbox{GL}(3)\times \hbox{GL}(2)$ $\hbox{L}$-functions II: The Eisenstein Case - https://arxiv.org/abs/2310.09419 - arXiv:2310.09419v2 Announce Type: replace -Abstract: This work is the second in a series, following Part I (Algebra Number Theory 18.10 (2024)) and preceding Part III (Math. Ann. 391.1 (2025)). We continue our investigation of spectral moments of $\hbox{GL}(3)\times \hbox{GL}(2)$ $\hbox{L}$-functions from the perspective of period integrals. Using an identity between two distinct periods for the $\hbox{GL}(3)$ Eisenstein series, we establish an exact Motohashi-type identity linking the shifted cubic moment of $\hbox{GL}(2)$ $\hbox{L}$-functions to the shifted fourth moment of $\hbox{GL}(1)$ $\hbox{L}$-functions. In addition, we offer a novel, intrinsic and automorphic account for the sources and symmetries of the full set of main terms for both moments, in agreement with the CFKRS Moment Conjectures (Proc. Lond. Math. Soc.(3) 91 (2005)). - oai:arXiv.org:2310.09419v2 - math.NT - math.CA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Chung-Hang Kwan - - - Profinite completions of topological operads - https://arxiv.org/abs/2312.12567 - arXiv:2312.12567v3 Announce Type: replace -Abstract: We show that the particular profinite completion used by Boavida-Horel-Robertson in their study of the Grothendieck-Teichm\"uller group fits in the framework of profinite completion as a left Quillen functor. More precisely, we construct a model category of profinite up-to-homotopy operads based on dendroidal objects in Quick's model category of profinite spaces and show that the construction of Boavida-Horel-Robertson extends to a left Quillen functor into this model category. We also characterize the underlying $\infty$-category of this model category and obtain a Dwyer-Kan style characterization of the weak equivalences between such profinite up-to-homotopy operads. Since this model category of profinite up-to-homotopy operads is Quillen equivalent to the one considered in our earlier paper "Profinite $\infty$-operads", we obtain analogous results in that setting. - oai:arXiv.org:2312.12567v3 - math.AT - math.CT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Thomas Blom, Ieke Moerdijk - - - Stable minimal hypersurfaces in $\mathbf{R}^5$ - https://arxiv.org/abs/2401.01492 - arXiv:2401.01492v3 Announce Type: replace -Abstract: We show that a complete, two-sided, stable minimal hypersurface in $\mathbf{R}^5$ is flat. - oai:arXiv.org:2401.01492v3 - math.DG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Otis Chodosh, Chao Li, Paul Minter, Douglas Stryker - - - A mathematical model of clonal hematopoiesis explaining phase transitions in chronic myeloid leukemia - https://arxiv.org/abs/2401.05316 - arXiv:2401.05316v2 Announce Type: replace -Abstract: This study presents a mathematical model describing cloned hematopoiesis in chronic myeloid leukemia (CML) through a nonlinear system of differential equations. The primary objective is to understand the progression from healthy hematopoiesis to the chronic and accelerated-acute phases in myeloid leukemia. The model incorporates intrinsic cellular division events in hematopoiesis and delineates the evolution of chronic myeloid leukemia into five compartments: cycling stem cells, quiescent stem cells, progenitor cells, differentiated cells and terminally differentiated cells. Our analysis reveals the existence of three distinct non-zero steady states within the dynamical system, representing healthy hematopoiesis, the chronic phase and the accelerated-acute stage of the disease. We investigate the local and global stability of these steady states and provide a characterization of the hematopoietic states based on this analysis. Additionally, numerical simulations are included to illustrate the theoretical results. - oai:arXiv.org:2401.05316v2 - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1093/imammb/dqaf004 - Mathematical Medicine and Biology: A Journal of the IMA (2025), 42(3), 253-288 - Lorand Gabriel Parajdi, Xue Bai, David Kegyes, Ciprian Tomuleasa - - - Orbifold modifications of complex analytic varieties - https://arxiv.org/abs/2401.07273 - arXiv:2401.07273v5 Announce Type: replace -Abstract: We prove that if $X$ is a compact complex analytic variety, which has quotient singularities in codimension 2, then there is a projective bimeromorphic morphism $f\colon Y\to X$, such that $Y$ has quotient singularities, and that the indeterminacy locus of $f^{-1}$ has codimension at least 3 in $X$. As an application, we deduce the Bogomolov-Gieseker inequality on orbifold Chern classes for stable reflexive coherent sheaves on compact K\"ahler varieties which have quotient singularities in codimension 2. - oai:arXiv.org:2401.07273v5 - math.AG - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/publicdomain/zero/1.0/ - Wenhao Ou - - - Bounds for the number of moves between pants decompositions, and between triangulations - https://arxiv.org/abs/2401.14233 - arXiv:2401.14233v2 Announce Type: replace -Abstract: Given two pants decompositions of a compact orientable surface $S$, we give an upper bound for their distance in the pants graph that depends logarithmically on their intersection number and polynomially on the Euler characteristic of $S$. As a consequence, we find an upper bound on the volume of the convex core of a maximal cusp (which is a hyperbolic structures on $S \times \mathbb{R}$ where given pants decompositions of the conformal boundary are pinched to annular cusps). As a further application, we give an upper bound for the Weil--Petersson distance between two points in the Teichm\"uller space of $S$ in terms of their corresponding short pants decompositions. Similarly, given two one-vertex triangulations of $S$, we give an upper bound for the number of flips and twist maps needed to convert one triangulation into the other. The proofs rely on using pre-triangulations, train tracks, and an algorithm of Agol, Hass, and Thurston. - oai:arXiv.org:2401.14233v2 - math.GT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Marc Lackenby, Mehdi Yazdi - - - Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions - https://arxiv.org/abs/2403.05712 - arXiv:2403.05712v5 Announce Type: replace -Abstract: The Rogers-Shephard and Zhang's projection inequalities are two reverse, affine isoperimetric-type inequalities for convex bodies. Following a classical work by Schneider, both inequalities have been extended to the so-called $m$th-order setting. In this work, we establish the $m$th-order analogues for these inequalities in the setting of log-concave functions. Our proof of the functional Zhang's projection inequality employs properties of the asymmetric LYZ body, significantly streamlining the argument and producing a novel approach for the case $m=1$. Furthermore, we introduce and analyze the radial mean bodies of a log-concave function, thereby providing a functional generalization of Gardner and Zhang's radial mean bodies. These are new even in the case $m=1$. Our development leverages an extension of Ball bodies, which may be of independent interest. - oai:arXiv.org:2403.05712v5 - math.MG - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dylan Langharst, Francisco Mar\'in Sola, Jacopo Ulivelli - - - Data-driven Stabilization of Nitsche's Method - https://arxiv.org/abs/2403.11632 - arXiv:2403.11632v2 Announce Type: replace -Abstract: The weak imposition of essential boundary conditions is an integral aspect of unfitted finite element methods, where the physical boundary does not in general coincide with the computational domain. In this regard, the symmetric Nitsche's method is a powerful technique that preserves the symmetry and variational consistency of the unmodified weak formulation. The stabilization parameter in Nitsche's method plays a crucial role in the stability of the resultant formulation, whose estimation is computationally intensive and dependent on the particular cut configuration using the conventional eigenvalue-based approach. In this work, we employ as model problem the finite cell method in which the need for the generation of a boundary-conforming mesh is circumvented by embedding the physical domain in a, typically regular, background mesh. We propose a data-driven estimate based on machine learning methods for the estimation of the stabilization parameter in Nitsche's method that offers an efficient constant-complexity alternative to the eigenvalue-based approach independent of the cut configuration. It is shown, using numerical benchmarks, that the proposed method can estimate the stabilization parameter accurately and is by far more computationally efficient. The data-driven estimate can be integrated into existing numerical codes with minimal modifications and thanks to the wide adoption of accelerators such as GPUs by machine learning frameworks, can be used with virtually no extra implementation cost on GPU devices, further increasing the potential for computational gains over the conventional eigenvalue-based estimate. The proposed model is tested on both Intel CPU as well as NVIDIA GPU hardware, showing that while it is already many times more efficient on the CPU compared to the eigenvalue-based estimate, its efficiency margin is even larger on modern GPU devices. - oai:arXiv.org:2403.11632v2 - math.NA - cs.NA - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - M. Saberi, L. Zhao, A. Vogel - - - Quasimorphisms of free products of racks and quandles - https://arxiv.org/abs/2404.14752 - arXiv:2404.14752v2 Announce Type: replace -Abstract: We show that the second bounded cohomology of the free product of racks and quandles is infinite-dimensional as a real vector space. This is similar to the case of groups. As a corollary, we show that the second bounded cohomology of the free rack and the free quandle is infinite-dimensional. We also give another proof of this corollary using homogeneous group quasimorphisms. - oai:arXiv.org:2404.14752v2 - math.GR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Masamitsu Aoki - - - Random coverage from within with variable radii, and Johnson-Mehl cover times - https://arxiv.org/abs/2405.17687 - arXiv:2405.17687v3 Announce Type: replace -Abstract: Given a compact planar region $A$, let $\tau_A$ be the (random) time it takes for the Johnson-Mehl tessellation of $A$ to be complete, i.e. the time it takes for $A$ to be fully covered by a spatial birth-growth process in $A$ with seeds arriving as a unit-intensity Poisson point process in $A \times [0,\infty)$, where upon arrival each seed grows at unit rate in all directions. We show that if $\partial A$ is smooth or polygonal then $\Pr [ \pi \tau_{sA}^3 - 6 \log s - 4 \log \log s \leq x]$ tends to $\exp(- (\frac{81}{4\pi})^{1/3} |A|e^{-x/3} -(\frac{9}{2\pi^2})^{1/3} |\partial A| e^{-x/6})$ in the large-$s$ limit; the second term in the exponent is due to boundary effects, the importance of which was not recognized in earlier work on this model. We present similar results in higher dimensions (where boundary effects dominate). These results are derived using new results on the asymptotic probability of covering $A$ with a high-intensity spherical Poisson Boolean model restricted to $A$ with grains having iid small random radii, which generalize recent work of the first author that dealt only with grains of deterministic radius. - oai:arXiv.org:2405.17687v3 - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Mathew D. Penrose, Frankie Higgs - - - On unsolvable equations of prime degree - https://arxiv.org/abs/2406.14221 - arXiv:2406.14221v2 Announce Type: replace -Abstract: Kronecker observed that either all roots or only one root of a solvable irreducible equation of odd prime degree with integer coefficients are real. This gives a possibility to construct specific examples of equations not solvable by radicals. A relatively elementary proof without using the full power of Galois theory is due to Weber. We give a rather short proof of Kronecker's theorem with a slightly different argument from Weber's. Several modern presentations of Weber's proof contain inaccuracies, which can be traced back to an error in the original proof. We discuss this error and how it can be corrected. - oai:arXiv.org:2406.14221v2 - math.NT - math.HO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Juliusz Brzezi\'nski, Jan Stevens - - - Normal forms for ordinary differential operators, I - https://arxiv.org/abs/2406.14414 - arXiv:2406.14414v4 Announce Type: replace -Abstract: In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible curves with vanishing cohomology groups. - This parametrisation is obtained with the help of normal forms - a notion we introduce in this paper. Namely, considering the ring of ordinary differential operators $D_1=K[[x]][\partial ]$ as a subring of a certain complete non-commutative ring $\hat{D}_1^{sym}$, the normal forms of differential operators mentioned here are obtained after conjugation by some invertible operator ("Schur operator"), calculated using one of the operators in a ring. Normal forms of commuting operators are polynomials with constant coefficients in the differentiation, integration and shift operators, which have a restricted finite order in each variable, and can be effectively calculated for any given commuting operators. - oai:arXiv.org:2406.14414v4 - math.AG - math-ph - math.MP - math.QA - math.RA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - J. Guo, A. B. Zheglov - - - A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells - https://arxiv.org/abs/2406.17491 - arXiv:2406.17491v4 Announce Type: replace -Abstract: Topology optimization problems usually feature multiple local minimizers. To guarantee convergence to local minimizers that perform best globally or to find local solutions that are desirable for practical applications due to easy manufacturability or aesthetic designs, it is important to compute multiple local minimizers of topology optimization problems. In this paper, we introduce a novel deflation approach to systematically find multiple local minimizers of general topology optimization problems. The approach is based on a penalization of previously found local solutions in the objective. We validate our approach on the so-called two-pipes five-holes example. Finally, we introduce a model for the topology optimization of bipolar plates of hydrogen electrolysis cells and demonstrate that our deflation approach enables the discovery of novel designs for such plates. - oai:arXiv.org:2406.17491v4 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1137/24M1670913 - SIAM J. Sci. Comput. 47, 2025 - Leon Baeck, Sebastian Blauth, Christian Leith\"auser, Ren\'e Pinnau, Kevin Sturm - - - Sample-based almost-sure quasi-optimal approximation in reproducing kernel Hilbert spaces - https://arxiv.org/abs/2407.06674 - arXiv:2407.06674v4 Announce Type: replace -Abstract: This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a sufficiently large test sample for estimating the approximation accuracy. Therefore, an approximation with a certified quasi-optimality factor is required. This article shows that such an approximation can be obtained when the sought function lies in a reproducing kernel Hilbert space (RKHS) and is to be approximated in a finite-dimensional linear subspace $\mathcal{V}_d$. However, selecting the sample points to minimise the quasi-optimality factor requires optimising over an infinite set of points and computing exact inner products in RKHS, which is often infeasible in practice. Extending results from optimal sampling for $L^2$ approximation, the present paper proves that random points, drawn independently from the Christoffel sampling distribution associated with $\mathcal{V}_d$, can yield a controllable quasi-optimality factor with high probability. Inspired by this result, a novel sampling scheme, coined subspace-informed volume sampling, is introduced and evaluated in numerical experiments, where it outperforms classical i.i.d. Christoffel sampling and continuous volume sampling. To reduce the size of such a random sample, an additional greedy subsampling scheme with provable suboptimality bounds is introduced. Our presentation is of independent interest to the inverse problems community, as it offers a simpler interpretation of the parametrised background data weak (PBDW) method. - oai:arXiv.org:2407.06674v4 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nando Hegemann, Anthony Nouy, Philipp Trunschke - - - Strong Embeddings of 3-Connected Cubic Planar Graphs on Surfaces of non-negative Euler Characteristic - https://arxiv.org/abs/2407.17972 - arXiv:2407.17972v2 Announce Type: replace -Abstract: Whitney proved that 3-connected planar graphs admit a unique embedding on the sphere. In contrast, Enami investigated embeddings of 3-connected cubic planar graphs on non-spherical surfaces with non-negative Euler characteristic. He established that such an embedding exists if and only if the dual graph contains a particular subgraph. Here, strong embeddings are investigated motivated by the cycle double cover conjecture and the relation to triangulated surfaces. We provide a complete characterization of strong embeddings on the projective plane, the torus, and the Klein bottle in terms of a distinguished subset of Enami's subgraphs. This characterization not only deepens the structural understanding of graph embeddings on non-spherical surfaces, but also establishes a robust foundation for computing cycle double covers. As a direct consequence, we derive explicit criteria that determine when a graph does not admit a strong embedding on these surfaces-offering new tools for both theoretical analysis and algorithmic applications. - oai:arXiv.org:2407.17972v2 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Meike Wei{\ss}, Alice C. Niemeyer - - - Bi-Lipschitz embedding metric triangles in the plane - https://arxiv.org/abs/2407.20019 - arXiv:2407.20019v2 Announce Type: replace -Abstract: A metric polygon is a metric space comprised of a finite number of closed intervals joined cyclically. The second-named author and Ntalampekos recently found a method to bi-Lipschitz embed an arbitrary metric triangle in the Euclidean plane with uniformly bounded distortion, which we call here the tripodal embedding. In this paper, we prove the sharp distortion bound $4\sqrt{7/3}$ for the tripodal embedding. We also give a detailed analysis of four representative examples of metric triangles: the intrinsic circle, the three-petal rose, tripods and the twisted heart. In particular, our examples show the sharpness of the tripodal embedding distortion bound and give a lower bound for the optimal distortion bound in general. Finally, we show the triangle embedding theorem does not generalize to metric quadrilaterals by giving a family of examples of metric quadrilaterals that are not bi-Lipschitz embeddable in the plane with uniform distortion. - oai:arXiv.org:2407.20019v2 - math.MG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xinyuan Luo, Matthew Romney, Alexandria L. Tao - - - Reflexive homology and involutive Hochschild homology as equivariant Loday constructions - https://arxiv.org/abs/2407.20082 - arXiv:2407.20082v4 Announce Type: replace -Abstract: For associative rings with anti-involution several homology theories exists, for instance reflexive homology as studied by Graves and involutive Hochschild homology defined by Fern\`andez-Val\`encia and Giansiracusa. We prove that the corresponding homology groups can be identified with the homotopy groups of an equivariant Loday construction of the one-point compactification of the sign-representation evaluated at the trivial orbit, if we assume that $2$ is invertible and if the underlying abelian group of the ring is flat. We also show a relative version where we consider an associative $k$-algebra with an anti-involution where $k$ is an arbitrary ground ring. - oai:arXiv.org:2407.20082v4 - math.AT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ayelet Lindenstrauss, Birgit Richter - - - Positive scalar curvature with point singularities - https://arxiv.org/abs/2407.20163 - arXiv:2407.20163v3 Announce Type: replace -Abstract: We show that in every dimension $n \geq 8$, there exists a smooth closed manifold $M^n$ which does not admit a smooth positive scalar curvature ("psc") metric, but $M$ admits an $\mathrm{L}^\infty$-metric which is smooth and has psc outside a singular set of codimension $\geq 8$. This provides counterexamples to a conjecture of Schoen. In fact, there are such examples of arbitrarily high dimension with only single point singularities. We also discuss related phenomena on exotic spheres and tori. In addition, we provide examples of $\mathrm{L}^\infty$-metrics on $\mathbb{R}^n$ for certain $n \geq 8$ which are smooth and have psc outside the origin, but cannot be smoothly approximated away from the origin by everywhere smooth Riemannian metrics of non-negative scalar curvature. This stands in precise contrast to established smoothing results via Ricci-DeTurck flow for singular metrics with stronger regularity assumptions. Finally, as a positive result, we describe a $\mathrm{KO}$-theoretic condition which obstructs the existence of $\mathrm{L}^\infty$-metrics that are smooth and of psc outside a finite subset. This shows that closed enlargeable spin manifolds do not carry such metrics. - oai:arXiv.org:2407.20163v3 - math.DG - math.GT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Simone Cecchini, Georg Frenck, Rudolf Zeidler - - - The weak Extension Principle - https://arxiv.org/abs/2407.20791 - arXiv:2407.20791v2 Announce Type: replace -Abstract: We prove a rigidity result for maps between \v{C}ech-Stone remainders under fairly mild forcing axioms. - oai:arXiv.org:2407.20791v2 - math.LO - math.GN - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1017/jsl.2025.10124 - Alessandro Vignati, Deniz Yilmaz - - - Detecting virtual homomorphisms via Banach metrics - https://arxiv.org/abs/2408.11543 - arXiv:2408.11543v2 Announce Type: replace -Abstract: We introduce the notion of "Banach metrics" on finitely generated infinite groups. This extends the notion of a Cayley graph (as a metric space). Our motivation comes from trying to detect the existence of virtual homomorphisms into Z, the additive group of integers. We show that detection of such homomorphisms through metric functional boundaries of Cayley graphs isn't always possible. However, we prove that it is always possible to do so through a metric functional boundary of some Banach metric on the group. - oai:arXiv.org:2408.11543v2 - math.GR - math.MG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-sa/4.0/ - Liran Ron-George, Ariel Yadin - - - Gromov-Hausdorff Distance for Directed Spaces - https://arxiv.org/abs/2408.14394 - arXiv:2408.14394v3 Announce Type: replace -Abstract: The Gromov-Hausdorff distance measures the similarity between two metric spaces by isometrically embedding them into an ambient metric space. We introduce an analogue of this distance for metric spaces endowed with directed structures. The directed Gromov-Hausdorff distance measures the distance between two extended metric spaces, where the new metric, defined on the same underlying space, is induced by the length of zigzag paths. This distance is then computed by isometrically embedding the directed metric spaces into an ambient directed space equipped with the zigzag distance. Analogously to the classical Gromov-Hausdorff distance, we also propose alternative formulations based on the distortion of d-maps and d-correspondences. However, unlike the classical case, these directed distances are not equivalent. - oai:arXiv.org:2408.14394v3 - math.AT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Lisbeth Fajstrup, Brittany Terese Fasy, Wenwen Li, Lydia Mezrag, Tatum Rask, Francesca Tombari, \v{Z}iva Urban\v{c}i\v{c} - - - A note on the unknotting number and the region unknotting number of weaving knots - https://arxiv.org/abs/2408.14938 - arXiv:2408.14938v3 Announce Type: replace -Abstract: A weaving knot is an alternating knot whose minimal diagram is a closed braid of a lattice-like pattern. In this paper, the warping degree of a braid diagram is defined, and upper bounds of the unknotting number and the region unknotting number for some families of weaving knots are given by diagrammatical and combinatorial examination of the warping degree of weaving knot diagrams. - oai:arXiv.org:2408.14938v3 - math.GT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ayaka Shimizu, Amrendra Gill, Sahil Joshi - - - Linear constellations in primes with arithmetic restrictions - https://arxiv.org/abs/2408.17441 - arXiv:2408.17441v3 Announce Type: replace -Abstract: We prove analogues of the theorem of Green and Tao on linear constellations in primes, in which the primes under consideration are restricted by certain arithmetic conditions. Our first main result is conditional upon Hooley's Riemann hypothesis and imposes the extra condition that the primes have prescribed primitive roots. Our second main result is unconditional and imposes the extra condition that the primes have prescribed Artin symbols in given Galois number fields. In the appendix we present an application of the second result in inverse Galois theory. - oai:arXiv.org:2408.17441v3 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Christopher Frei, Joachim K\"onig, Magdal\'ena Tinkov\'a - - - Multifractal spectrum of branching random walks on free groups - https://arxiv.org/abs/2409.01346 - arXiv:2409.01346v2 Announce Type: replace -Abstract: A symmetric branching random walk (BRW) on a free group $\mathbb{F}$ is transient if and only if the mean offspring number $r$ does not exceed $R$, the reciprocal of the spectral radius of the underlying random walk. In this regime, the limit set $\Lambda_r$ -- consisting of all ends of $\mathbb{F}$ to which the BRW's particle trajectories converge -- is a proper random subset of the boundary $\partial \mathbb{F}$. Hueter and Lalley (2000) determined the Hausdorff dimension of $\Lambda_r$ and proved that $\dim_{\mathrm{H}} \Lambda_r \le (1/2)\dim_{\mathrm{H}} \partial \mathbb{F}$, with equality possible only when $r = R$. - In this paper, we further extend this study by conducting a multifractal analysis of the limit set $\Lambda_r$. We obtain the Hausdorff dimensions of the subfractals $\Lambda_r(\alpha) \subset \Lambda_r$, which consist of all ends of $\mathbb{F}$ approached by particle trajectories escaping at rate $\alpha \in [0,1]$. Notably, there exists a unique $\alpha(r) \in [0,1]$ such that \[ - \dim_{\mathrm{H}} \Lambda_r = \dim_{\mathrm{H}} \Lambda_r(\alpha(r)). \] Moreover, an interesting phase transition occurs: $\alpha(r) > 0$ for $r < R$ while $\alpha(R) = 0$. - oai:arXiv.org:2409.01346v2 - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shuwen Lai, Heng Ma, Longmin Wang - - - Monoidal categorification on open Richardson varieties - https://arxiv.org/abs/2409.04715 - arXiv:2409.04715v4 Announce Type: replace -Abstract: In this paper, we show that the subcategory $\mathscr{C}_{w,v}$ of modules over quiver Hecke algebras is a monoidal categorification of the coordinate ring of any open Richardson variety of Dynkin types after inverting the frozen cluster variables. - oai:arXiv.org:2409.04715v4 - math.RT - math.QA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Yingjin Bi - - - Variational closures for composite homogenised fluid flows - https://arxiv.org/abs/2409.10408 - arXiv:2409.10408v3 Announce Type: replace -Abstract: Homogenisation theory has seen recent applications in deriving stochastic transport models for fluid dynamics. In this work, we first derive the stochastic Lagrange-to-Euler map that underpins stochastic transport noise in fluid dynamics as the homogenisation limit of a parameterised flow map decomposing into rapidly fluctuating and slow components. Specifically, we prove convergence of this parameterised flow map to a scale-separated limit under the assumptions of a weak invariance principle for the rapidly fluctuating component and path continuity for the slow component. In this limit, the rapidly fluctuating component converges to a stochastic flow of diffeomorphisms that transforms the full flow dynamics into an SDE-governed stochastic flow through composition, while the slow component requires closure. - Our second contribution formulates two distinct variational closures for the slow component of the homogenised flow that exploit the composite structure of the stochastic flow. For the first closure, the critical points of a new variational principle satisfy a system of random-coefficient PDEs, which can be transformed into a system of stochastic PDEs via the coadjoint action of the stochastic flow map obtained from homogenising the fluctuating component. We show that these equations coincide with the stochastic Euler-Poincar\'e equations previously derived in Holm, Proc. Royal Soc. (2015). For the second closure, we modify the assumptions on the slow component and the associated variational principle to derive averaged models inspired by previous work on mean flow dynamics such as the Generalised Lagrangian Mean. - oai:arXiv.org:2409.10408v3 - math-ph - math.DS - math.MP - math.PR - physics.flu-dyn - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Theo Diamantakis, Ruiao Hu, James-Michael Leahy - - - Causal Discovery in Nonlinear Dynamical Systems using Koopman Operators - https://arxiv.org/abs/2410.10103 - arXiv:2410.10103v2 Announce Type: replace -Abstract: We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that causal mechanisms manifest as particular flows of observables between function subspaces. While the flow map definition is a clear generalization of the standard definition of causal mechanism given in the structural causal model framework, the flow maps are complicated objects that are not tractable to work with in practice. By contrast, the equivalent Koopman definition lends itself to a straightforward data-driven algorithm that can quantify multivariate causal relations in high-dimensional nonlinear dynamical systems. The coupled Rossler system provides examples and demonstrations throughout our exposition. We also demonstrate the utility of our data-driven Koopman causality measure by identifying causal flow in the Lorenz 96 system. We show that the causal flow identified by our data-driven algorithm agrees with the information flow identified through a perturbation propagation experiment. Our work provides new theoretical insights into causality for nonlinear dynamical systems, as well as a new toolkit for data-driven causal analysis. - oai:arXiv.org:2410.10103v2 - math.DS - physics.comp-ph - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Adam Rupe, Derek DeSantis, Craig Bakker, Parvathi Kooloth, Jian Lu - - - A new hierarchy for complex plane curves - https://arxiv.org/abs/2410.11479 - arXiv:2410.11479v3 Announce Type: replace -Abstract: We define the type of a plane curve as the initial degree of the corresponding Bourbaki ideal. Then we show that this invariant behaves well with respect to the union of curves. Curves of type $0$ are precisely the free curves, while curves of type $1$ are the plus-one generated curves. In this paper, we first show that line arrangements and conic-line arrangements can exhibit all the theoretically possible types. In the second part, we study the properties of the curves of type $2$ and construct families of line arrangements and conic-line arrangements of this type. - oai:arXiv.org:2410.11479v3 - math.AG - math.AC - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Takuro Abe, Alexandru Dimca, Piotr Pokora - - - Improving the Accuracy of DC Optimal Power Flow Formulations via Parameter Optimization - https://arxiv.org/abs/2410.11725 - arXiv:2410.11725v2 Announce Type: replace -Abstract: DC Optimal Power Flow (DC-OPF) problems optimize the generators' active power setpoints while satisfying constraints based on the DC power flow linearization. The computational tractability advantages of DC-OPF problems come at the expense of inaccuracies relative to AC Optimal Power Flow (AC-OPF) problems that accurately model the nonlinear steady-state behavior of power grids. This paper proposes an algorithm that significantly improves the accuracy of the generators' active power setpoints from DC-OPF problems with respect to the corresponding AC-OPF problems over a specified range of operating conditions. Using sensitivity information in a machine learning-inspired methodology, this algorithm tunes coefficient and bias parameters in the DC power flow approximation to improve the accuracy of the resulting DC-OPF solutions. Employing the Truncated Newton Conjugate-Gradient (TNC) method -- a Quasi-Newton optimization technique -- this parameter tuning occurs during an offline training phase, with the resulting parameters then used in online computations. Numerical results underscore the algorithm's efficacy with accuracy improvements in squared two-norm and $\infty$-norm losses of up to $90\%$ and $79\%$, respectively, relative to traditional DC-OPF formulations. - oai:arXiv.org:2410.11725v2 - math.OC - cs.SY - eess.SY - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Babak Taheri, Daniel K. Molzahn - - - A determinantal formula for cluster variables in cluster algebras from surfaces - https://arxiv.org/abs/2410.14554 - arXiv:2410.14554v2 Announce Type: replace -Abstract: For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weighted biadjacency matrix of the associated snake graphs, thus circumventing the enumeration of their perfect matchings. - oai:arXiv.org:2410.14554v2 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Javier De Loera - - - Effective bounds on characterising slopes for all knots - https://arxiv.org/abs/2410.24209 - arXiv:2410.24209v2 Announce Type: replace -Abstract: A slope $p/q$ is characterising for a knot $K \subset \mathbb{S}^3$ if the orientation-preserving homeomorphism type of the manifold $\mathbb{S}^3_K(p/q)$ obtained by performing Dehn surgery of slope $p/q$ along $K$ uniquely determines the knot $K$. We combine new applications of results from hyperbolic geometry with previous individual work of the authors to determine, for any given knot $K$, an explicit bound $\mathcal{C}(K)$ such that $|q| > \mathcal{C}(K)$ implies that $p/q$ is a characterising slope for $K$. Furthermore, we find an optimal such $\mathcal{C}(K)$ for certain satellite knots with winding number zero patterns. - oai:arXiv.org:2410.24209v2 - math.GT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Patricia Sorya, Laura Wakelin - - - Revisiting the Lavrentiev Phenomenon in One Dimension - https://arxiv.org/abs/2411.16296 - arXiv:2411.16296v3 Announce Type: replace -Abstract: We clarify and extend insights from Lavrentiev's seminal paper. We examine the original theorem on the absence of the Lavrentiev's phenomenon and a counterexample offering a detailed analysis of its proof and providing a new, concise, and complete reasoning. In the appendix, we also provide additional details to supplement the original proof. - oai:arXiv.org:2411.16296v3 - math.CA - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Wiktor Wichrowski - - - A bi-fidelity method for the uncertain Vlasov-Poisson system near quasineutrality in an asymptotic-preserving particle-in-cell framework - https://arxiv.org/abs/2412.05663 - arXiv:2412.05663v2 Announce Type: replace -Abstract: In this paper, we study the Vlasov-Poisson system with massless electrons (VPME) near quasineutrality and with uncertainties. Based on the idea of reformulation on the Poisson equation by [P. Degond et.al., $\textit{Journal of Computational Physics}$, 229 (16), 2010, pp. 5630--5652], we first consider the deterministic problem and develop an efficient asymptotic-preserving particle-in-cell (AP-PIC) method to capture the quasineutral limit numerically, without resolving the discretizations subject to the small Debye length in plasma. The main challenge and difference compared to previous related works is that we consider the nonlinear Poisson in the VPME system which contains $e^{\phi}$ (with $\phi$ being the electric potential) and provide an explicit scheme. In the second part, we extend to study the uncertainty quantification (UQ) problem and develop an efficient bi-fidelity method for solving the VPME system with multidimensional random parameters, by choosing the Euler-Poisson equation as the low-fidelity model. Several numerical experiments are shown to demonstrate the asymptotic-preserving property of our deterministic solver and the effectiveness of our bi-fidelity method for solving the model with random uncertainties. - oai:arXiv.org:2412.05663v2 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Guangwei Liu, Liu Liu, Yanli Wang - - - Beyond Minimax Optimality: A Subgame Perfect Gradient Method - https://arxiv.org/abs/2412.06731 - arXiv:2412.06731v3 Announce Type: replace -Abstract: The study of convex optimization has historically been concerned with worst-case convergence rates. The development of the Optimized Gradient Method (OGM), due to \citet{drori2012PerformanceOF,Kim2016optimal}, marked a major milestone in this study, as OGM achieves the optimal worst-case convergence rate among all first-order methods for unconstrained smooth convex optimization. In order to examine the possibility of obtaining stronger convergence guarantees, we will consider algorithms with \emph{dynamic} convergence rates, which may improve as additional first-order information is revealed. Our main contribution is the development of an algorithm, the Subgame Perfect Gradient Method (SPGM), which refines OGM to make use of the full history of first-order information. We show that SPGM is \emph{dynamically optimal}, in the sense that in each iteration, no other algorithm can offer a strictly better convergence rate on all functions which agree with the observed first-order information up to that iteration. We formalize this notion of dynamic optimality using the game-theoretic notion of a subgame perfect equilibrium. We conclude our study with preliminary numerical experiments showing that SPGM strongly outperforms OGM. - oai:arXiv.org:2412.06731v3 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Benjamin Grimmer, Kevin Shu, Alex L. Wang - - - Decay of solutions to one-dimensional inhomogeneous nonlinear Schr\"odinger equations - https://arxiv.org/abs/2412.08272 - arXiv:2412.08272v2 Announce Type: replace -Abstract: We investigate the decay estimates of global solutions for a class of one-dimensional inhomogeneous nonlinear Schr\"odinger equations. While most existing results focus on spatial dimensions $d\geq2$, the decay properties in one dimension remain less explored due to the absence of effective Morawetz inequalities. For equations without external potential, by establishing a localized Virial-Morawetz identity, we derive decay estimates in the context of the $L^r$-norm for global solutions within a compact domain as a time subsequence approaches infinity. This decay result can be applied to obtain a criterion for energy scattering. Additionally, by establishing another type of Virial-Morawetz identity under more strict conditions, we demonstrate the decay result for odd solutions for any time sequence that approaches infinity. Utilizing some results about bound states proved by Barry Simon, we also show that similar decay results hold for the global odd solutions of equations with suitable external potentials that contain inverse power type and Yukawa-type potentials. - oai:arXiv.org:2412.08272v2 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhi-Yuan Cui, Yuan Li, Dun Zhao - - - Huygens and $\pi$ - https://arxiv.org/abs/2412.10880 - arXiv:2412.10880v3 Announce Type: replace -Abstract: The Dutch scientist Christiaan Huygens refined Archimedes' celebrated geometrical computation of $\pi$ to its highest point. Yet the rich content of his beautiful treatise \emph{De circuli magnitudine inventa} (1654) has apparently never been presented in modern form. Here we offer a detailed and contemporary development of several of his most striking results. We also make a historical conjecture concerning Archimedes' trisection figure. - oai:arXiv.org:2412.10880v3 - math.HO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mark B. Villarino, Joseph C. Varilly - - - Discrete Poincar\'e inequalities: a review on proofs, equivalent formulations, and behavior of constants - https://arxiv.org/abs/2412.11796 - arXiv:2412.11796v2 Announce Type: replace -Abstract: We investigate discrete Poincar\'e inequalities on piecewise polynomial subspaces of the Sobolev spaces H(curl) and H(div) in three space dimensions. We characterize the dependence of the constants on the continuous-level constants, the shape regularity and cardinality of the underlying tetrahedral mesh, and the polynomial degree. One important focus is on meshes being local patches (stars) of tetrahedra from a larger tetrahedral mesh. We also review various equivalent results to the discrete Poincar\'e inequalities, namely stability of discrete constrained minimization problems, discrete inf-sup conditions, bounds on operator norms of piecewise polynomial vector potential operators (Poincar\'e maps), and existence of graph-stable commuting projections. - oai:arXiv.org:2412.11796v2 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - 10.1093/imanum/draf089 - Alexandre Ern, Johnny Guzm\'an, Pratyush Potu, Martin Vohral\'ik - - - Real and Complex Analysis: Solutions to Problems in Amer. Math. Monthly, Math. Magazine, College Math. J., Elemente der Math., Crux Math., EMS Newsletter, Math. Gazette - https://arxiv.org/abs/2501.05096 - arXiv:2501.05096v2 Announce Type: replace -Abstract: In this arxiv-post I present my solutions (published or not) to Problems that appeared in Amer. Math. Monthly, Math. Magazine, Elemente der Mathematik and CRUX, that were mostly done in collaboration with Rudolf Rupp. Some of them (including a few own proposals which were published) were also done in cooperation with Rainer Br\"uck, Bikash Chakraborty, Pamela Gorkin, Gerd Herzog, J\'er\^ome No\"el, Peter Pflug and Amol Sasane. - oai:arXiv.org:2501.05096v2 - math.HO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Raymond Mortini - - - Trace Reconstruction of First-Order Reed-Muller Codewords Using Run Statistics - https://arxiv.org/abs/2501.11393 - arXiv:2501.11393v3 Announce Type: replace -Abstract: In this paper, we derive an expression for the expected number of runs in a trace of a binary sequence $x \in \{0,1\}^n$ obtained by passing $x$ through a deletion channel that independently deletes each bit with probability $q$. We use this expression to show that if $x$ is a codeword of a first-order Reed-Muller code, and the deletion probability $q$ is 1/2, then $x$ can be reconstructed, with high probability, from $\tilde{O}(n^2)$ many of its traces. - oai:arXiv.org:2501.11393v3 - cs.IT - math.IT - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shiv Pratap Singh Rathore, Navin Kashyap - - - Twisted torus knots with Horadam parameters - https://arxiv.org/abs/2501.17850 - arXiv:2501.17850v4 Announce Type: replace -Abstract: Sangyop Lee has done much work to determine the knot types of twisted torus knots, including classifying the twisted torus knots which are the unknot. Among the unknotted twisted torus knots are those of the form $K(F_{n+2}, F_n, F_{n+1}, -1)$, where $F_i$ is the $i$th Fibonacci number. Here, we consider twisted torus knots with parameters that are defined recursively, similarly to the Fibonacci sequence. We call these Horadam parameters, after the generalization of the Fibonacci sequence introduced by A.F. Horadam. Here, we provide families of twisted torus knots that generalize Lee's work with Horadam parameters. Additionally, we provide lists of primitive/primitive and primitive/Seifert twisted torus knots and connect these lists to the Horadam twisted torus knots. - oai:arXiv.org:2501.17850v4 - math.GT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Brandy Doleshal - - - The number of smooth varieties in an MMP on a 3-fold of Fano type - https://arxiv.org/abs/2502.01370 - arXiv:2502.01370v3 Announce Type: replace -Abstract: In this paper, we prove that for a threefold of Fano type $X$ and a movable $\mathbb{Q}$-Cartier Weil divisor $D$ on $X$, the number of smooth varieties that arise during the running of a $D$-MMP is bounded by $1 + h^1(X, 2D)$. Additionally, we prove a partial converse to the Kodaira vanishing theorem for a movable divisor on a threefold of Fano type. - oai:arXiv.org:2502.01370v3 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Donghyeon Kim - - - Hardy-Littlewood maximal, generalized Bessel-Riesz and generalized fractional integral operators in generalized Morrey and $BMO_\phi$ spaces associated with Dunkl operator on the real line - https://arxiv.org/abs/2502.14390 - arXiv:2502.14390v3 Announce Type: replace -Abstract: The analysis of Morrey spaces, generalized Morrey spaces and $BMO_\phi$ spaces related to the Dunkl operators on $\mathbb{R}$ are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz operators, generalized Bessel-Riesz operators, and generalized fractional integral operators associated with Dunkl operators on $\mathbb{R}$ in the generalized Dunkl-type Morrey spaces. Further, we derive the boundedness of the modified version of the generalized fractional integral operators associated with the Dunkl operators on $\mathbb{R}$ in Dunkl-type $BMO_\phi$ spaces. - oai:arXiv.org:2502.14390v3 - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Sumit Parashar, Saswata Adhikari - - - Contact big fiber theorems - https://arxiv.org/abs/2503.04277 - arXiv:2503.04277v3 Announce Type: replace -Abstract: We prove contact big fiber theorems, analogous to the symplectic big fiber theorem by Entov and Polterovich, using symplectic cohomology with support. Unlike in the symplectic case, the validity of the statements requires conditions on the closed contact manifold. One such condition is to admit a Liouville filling with non-zero symplectic cohomology. In the case of Boothby-Wang contact manifolds, we prove the result under the condition that the Euler class of the circle bundle, which is the negative of an integral lift of the symplectic class, is not an invertible element in the quantum cohomology of the base symplectic manifold. As applications, we obtain new examples of rigidity of intersections in contact manifolds and also of contact non-squeezing. - oai:arXiv.org:2503.04277v3 - math.SG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-sa/4.0/ - Yuhan Sun, Igor Uljarevic, Umut Varolgunes - - - Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization - https://arxiv.org/abs/2503.15093 - arXiv:2503.15093v3 Announce Type: replace -Abstract: This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications. To tackle these optimization problems, inspired by recent results, we introduce the \emph{proportional--integral proximal gradient dynamics} (PI--PGD): a closed-loop system where the Lagrange multipliers are control inputs and states are the problem decision variables. First, we establish the equivalence between the stationary points of the minimization problem and the equilibria of the PI--PGD. Then for the case of affine constraints, by leveraging tools from contraction theory we give a comprehensive convergence analysis for the dynamics, showing linear--exponential convergence towards the equilibrium. That is, the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. Our findings are illustrated numerically on a set of representative examples, which include an exploratory application to nonlinear equality constraints. - oai:arXiv.org:2503.15093v3 - math.OC - cs.SY - eess.SY - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Veronica Centorrino, Francesca Rossi, Francesco Bullo, Giovanni Russo - - - Hereditary completeness for systems of exponentials in weighted $L^2$-spaces - https://arxiv.org/abs/2503.18131 - arXiv:2503.18131v2 Announce Type: replace -Abstract: We prove that for a weight $w$, which has at least polynomial decay, there exists a complete and minimal system $\{e^{i\lambda_n t}\}_{n\in \mathbb{N}}$ of exponentials in weighted space $L^2(w)$ on $(-\pi,\pi)$, which is not hereditarily complete. - oai:arXiv.org:2503.18131v2 - math.CV - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Andrei V. Semenov - - - Rough Heston model as the scaling limit of bivariate cumulative heavy-tailed INAR processes: Weak-error bounds and option pricing - https://arxiv.org/abs/2503.18259 - arXiv:2503.18259v4 Announce Type: replace -Abstract: This paper links nearly unstable, heavy-tailed \emph{bivariate cumulative} INAR($\infty$) processes to the rough Heston model via a discrete scaling limit, extending scaling-limit techniques beyond Hawkes processes and providing a microstructural mechanism for rough volatility and leverage effect. Computationally, we simulate the \emph{approximating INAR($\infty$)} sequence rather than discretizing the Volterra SDE, and implement the long-memory convolution with a \emph{divide-and-conquer FFT} (CDQ) that reuses past transforms, yielding an efficient Monte Carlo engine for \emph{European options} and \emph{path-dependent options} (Asian, lookback, barrier). We further derive finite-horizon \emph{weak-error bounds} for option pricing under our microstructural approximation. Numerical experiments show tight confidence intervals with improved efficiency; as $\alpha \to 1$, results align with the classical Heston benchmark, where $\alpha$ is the roughness specification. Using the simulator, we also study the \emph{implied-volatility surface}: the roughness specification ($\alpha<1$) reproduces key empirical features -- most notably the steep short-maturity ATM skew with power-law decay -- whereas the classical model produces a much flatter skew. - oai:arXiv.org:2503.18259v4 - math.PR - q-fin.MF - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Yingli Wang, Zhenyu Cui, Lingjiong Zhu - - - A Polynomial-Time Algorithm for Variational Inequalities under the Minty Condition - https://arxiv.org/abs/2504.03432 - arXiv:2504.03432v2 Announce Type: replace -Abstract: Solving variational inequalities (SVIs) is a foundational problem at the heart of optimization. However, this expressivity comes at the cost of computational hardness. As a result, most research has focused on carving out specific subclasses that elude those intractability barriers. A classical property that goes back to the 1960s is the Minty condition, which postulates that the Minty VI (MVI) problem admits a solution. - In this paper, we establish the first polynomial-time algorithm -- that is, with complexity growing polynomially in the dimension $d$ and $\log(1/\epsilon)$ -- for solving $\epsilon$-SVIs for Lipschitz continuous mappings under the Minty condition. Prior approaches either incurred an exponentially worse dependence on $1/\epsilon$ or made restrictive assumptions. To do so, we introduce a new variant of the ellipsoid algorithm whereby separating hyperplanes are obtained after taking a gradient descent step from the center of the ellipsoid. It succeeds even though the set of SVIs can be nonconvex and not fully dimensional. Moreover, when our algorithm is applied to an instance with no MVI solution and fails to identify an SVI solution, it produces a succinct certificate of MVI infeasibility. We also show that deciding whether the Minty condition holds is $\mathsf{coNP}$-complete, thereby establishing that the disjunction of those two problems is polynomial-time solvable even though each problem is individually intractable. - We provide several extensions and new applications of our main results. Most notably, we obtain the first polynomial-time algorithms for i) globally minimizing a (potentially nonsmooth) quasar-convex function, and ii) computing Nash equilibria in multi-player harmonic games. Finally, in two-player general-sum concave games, we give the first polynomial-time algorithm that outputs either a Nash equilibrium or a strict coarse correlated equilibrium. - oai:arXiv.org:2504.03432v2 - math.OC - cs.GT - cs.LG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ioannis Anagnostides, Gabriele Farina, Tuomas Sandholm, Brian Hu Zhang - - - Profinite Direct Sums with Applications to Profinite Groups of Type $\Phi_R$ - https://arxiv.org/abs/2504.05182 - arXiv:2504.05182v2 Announce Type: replace -Abstract: We show that the "profinite direct sum" is a good notion of infinite direct sums for profinite modules having properties similar to direct sums of abstract modules. For example, the profinite direct sum of projective modules is projective, and there is a Mackey's Formula for profinite modules described using these sums. As an application, we prove that the class of profinite groups of type $\Phi_R$ is closed under subgroups. - oai:arXiv.org:2504.05182v2 - math.RA - math.CT - math.GR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jiacheng Tang - - - A geometric analysis of the Bazykin-Berezovskaya predator-prey model with Allee effect in an economic framework - https://arxiv.org/abs/2504.10355 - arXiv:2504.10355v3 Announce Type: replace -Abstract: We study a fast-slow version of the Bazykin-Berezovskaya predator-prey model with Allee effect evolving on two timescales, through the lenses of Geometric Singular Perturbation Theory (GSPT). The system we consider is in non-standard form. We completely characterize its dynamics, providing explicit threshold quantities to distinguish between a rich variety of possible asymptotic behaviors. Moreover, we propose numerical results to illustrate our findings. Lastly, we comment on the real-world interpretation of these results, in an economic framework and in the context of predator-prey models. - oai:arXiv.org:2504.10355v3 - math.DS - q-bio.PE - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jacopo Borsotti, Mattia Sensi - - - High-dimensional dynamics in low-dimensional networks - https://arxiv.org/abs/2504.13727 - arXiv:2504.13727v3 Announce Type: replace -Abstract: Many networks in nature and applications have an approximate low-rank structure in the sense that their connectivity structure is dominated by a few dimensions. It is natural to expect that dynamics on such networks would also be low-dimensional. Indeed, theoretical results show that low-rank networks produce low-dimensional dynamics whenever the network is isolated from external perturbations or input. However, networks in nature are rarely isolated. Here, we study the dimensionality of dynamics in recurrent networks with low-dimensional structure driven by high-dimensional inputs or perturbations. We find that dynamics in such networks can be high- or low-dimensional and we derive precise conditions on the network structure under which dynamics are high-dimensional. In many low-rank networks, dynamics are suppressed in directions aligned with the network's low-rank structure, a phenomenon we term ``low-rank suppression.'' We show that several low-rank network structures arising in nature satisfy the conditions for generating high-dimensional dynamics and low-rank suppression. Our results clarify important, but counterintuitive relationships between a recurrent network's connectivity structure and the structure of the dynamics it generates. - oai:arXiv.org:2504.13727v3 - math.DS - math-ph - math.MP - q-bio.NC - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Yue Wan, Robert Rosenbaum - - - Asynchronous Push-sum Dual Gradient Algorithm in Distributed Model Predictive Control - https://arxiv.org/abs/2504.18941 - arXiv:2504.18941v3 Announce Type: replace -Abstract: This paper studies the distributed model predictive control (DMPC) problem for distributed discrete-time linear systems with both local and global constraints over directed communication networks. We establish an optimization problem to formulate the DMPC policy, including the design of terminal ingredients. To cope with the global constraint, we transform the primal optimization problem into its dual problem. Then, we propose a novel asynchronous push-sum dual gradient (APDG) algorithm with an adaptive step-size scheme to solve this dual problem in a fully asynchronous distributed manner. The proposed algorithm does not require synchronous waiting and any form of coordination, which greatly improves solving efficiency. We prove that the APDG algorithm converges at an R-linear rate as long as the step-size does not exceed the designed upper bound. Furthermore, we develop a distributed termination criterion to terminate the APDG algorithm when its output solution satisfies the specified suboptimality and the global constraint, thereby avoiding an infinite number of iterations. The recursive feasibility and the stability of the closed-loop system are also established. Finally, a numerical example is provided to clarify and validate our theoretical findings. - oai:arXiv.org:2504.18941v3 - math.OC - cs.SY - eess.SY - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pengbiao Wang, Xuemei Ren, Dongdong Zheng - - - The Chromatic Symmetric Function for Unicyclic Graphs - https://arxiv.org/abs/2505.06486 - arXiv:2505.06486v2 Announce Type: replace -Abstract: Motivated by the question of which structural properties of a graph can be recovered from the chromatic symmetric function (CSF), we study the CSF of connected unicyclic graphs. While it is known that there can be non-isomorphic unicyclic graphs with the same CSF, we find experimentally that such examples are rare for graphs with up to 17 vertices. In fact, in many cases we can recover data such as the number of leaves, number of internal edges, cycle size, and number of attached non-trivial trees, by extending known results for trees to unicyclic graphs. These results are obtained by analyzing the CSF of a connected unicyclic graph in the $\textit{star-basis}$ using the deletion-near-contraction (DNC) relation developed by Aliste-Prieto, Orellana and Zamora, and computing the "leading" partition, its coefficient, as well as coefficients indexed by hook partitions. We also give explicit formulas for star-expansions of several classes of graphs, developing methods for extracting coefficients using structural properties of the graph. - oai:arXiv.org:2505.06486v2 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Aram Bingham, Lisa Johnston, Colin Lawson, Rosa Orellana, Jianping Pan, Chelsea Sato - - - Critical Exponent Rigidity for $\Theta-$positive Representations - https://arxiv.org/abs/2505.17559 - arXiv:2505.17559v3 Announce Type: replace -Abstract: We prove for a $\Theta-$positive representation from a discrete subgroup $\Gamma\subset \mathsf{PSL}(2,\mathbb{R})$, the critical exponent for any $\alpha\in \Theta$ is not greater than one. When $\Gamma$ is geometrically finite, the equality holds if and only if $\Gamma$ is a lattice. - oai:arXiv.org:2505.17559v3 - math.DG - math.DS - math.GR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhufeng Yao - - - Consecutive collision orbits in the restricted three-body problem above the first critical energy value - https://arxiv.org/abs/2506.01735 - arXiv:2506.01735v3 Announce Type: replace -Abstract: In this paper, we study the planar circular restricted three-body problem for energy levels slightly above the first critical value. We first observe that the energy hypersurfaces in the Birkhoff regularization corresponding to these energy levels are of contact type. Then, using a version of Rabinowitz Floer homology, we establish the existence of either a periodic symmetric collision orbit or infinitely many symmetric consecutive collision orbits. Furthermore, by an analytic continuation argument, for generic mass ratios and energy levels, we prove that there is no periodic symmetric collision orbit with odd number of collisions. This in turn implies the existence of at least two symmetric consecutive collision orbits. - oai:arXiv.org:2506.01735v3 - math.SG - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Jungsoo Kang, Kevin Ruck - - - Dirichlet kernel density estimation for strongly mixing sequences on the simplex - https://arxiv.org/abs/2506.08816 - arXiv:2506.08816v2 Announce Type: replace -Abstract: This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong mixing conditions. We establish rigorous results for the asymptotic normality and mean squared error of these estimators, extending previous findings from the independent and identically distributed (iid) context to the more general setting of strongly mixing processes. To demonstrate its practical utility, the estimator is applied to monthly market-share compositions of several Renault vehicle classes over a twelve-year period, with bandwidth selection performed via leave-one-out least squares cross-validation. Our findings underscore the reliability and strength of Dirichlet kernel techniques when applied to temporally dependent compositional data. - oai:arXiv.org:2506.08816v2 - math.ST - stat.ME - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hanen Daayeb, Salah Khardani, Fr\'ed\'eric Ouimet - - - Trigonal Curve with Trigonal Deformation of Maximal Rank - https://arxiv.org/abs/2506.11450 - arXiv:2506.11450v3 Announce Type: replace -Abstract: By extending methods of Favale-Pirola arXiv:2108.02157 and Gonz\'alez-Alonso-Torelli arXiv:2402.15158 to toric surfaces via toric Jacobian ring, we are able to show there exists trigonal curve with trigonal deformation of rank $g$ for $g=5,7,9,11,13,15$ by giving an explicit example. Also, we give a computable criterion to determine whether a nondegenerate ample section of toric surface has first order deformation of rank $g$ within the linear system. - oai:arXiv.org:2506.11450v3 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jiacheng Zhang - - - The Fourier spectral approach to the spatial discretization of quasilinear hyperbolic systems - https://arxiv.org/abs/2507.00516 - arXiv:2507.00516v2 Announce Type: replace -Abstract: We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability estimates that grant spectral convergence of the (spatially) semi-discretized solutions towards the corresponding continuous solution provided that the underlying system satisfies some suitable structural assumptions. We consider a setting with sharp low-pass filters and a setting with smooth low-pass filters and argue that - at least theoretically - smooth low-pass filters are operable on a larger class of systems. While our theoretical results are supported with numerical evidence, we also pinpoint some behavior of the numerical method that currently has no theoretical explanation. - oai:arXiv.org:2507.00516v2 - math.NA - cs.NA - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vincent Duch\^ene, Johanna Ulvedal Marstrander - - - An efficient asymptotic preserving Monte Carlo method for frequency-dependent radiative transfer equations - https://arxiv.org/abs/2507.02392 - arXiv:2507.02392v2 Announce Type: replace -Abstract: In this paper, we develop an efficient asymptotic-preserving (AP) Monte Carlo (MC) method for frequency-dependent radiative transfer equations (RTEs), which is based on the AP-MC method proposed for the gray RTEs in \cite{shi2023efficient}. We follow the characteristics-based approach by Zhang et al. \cite{zhang2023asymptotic} to get a reformulated model, which couples a low dimension convection-diffusion-type equation for macroscopic quantities with a high dimension transport equation for the radiative intensity. - To recover the correct free streaming limit due to frequency-dependency, we propose a correction to the reformulated macroscopic equation. - The macroscopic system is solved using a hybrid method: - convective fluxes are handled by a particle-based MC method, while diffusive fluxes are treated implicitly with central difference. - To address the nonlinear coupling between radiative intensity and the Planck function across multiple frequency groups, we adopt a Picard iteration with a predictor-corrector procedure, which decouples a global nonlinear system into a linear system restricted to spatial dimension (independent of frequency) with scalar algebraic nonlinear equations. - Once the macroscopic update is done, the transport equation, with a known emission source provided by the macroscopic variables, is efficiently solved using an implicit MC method. This approach enables larger time steps independent of the speed of light and also the frequency across a wide range, significantly enhancing computational efficiency, especially for frequency-dependent RTEs. - Formal AP analysis in the diffusive scaling is established. Numerical experiments are performed to demonstrate the high efficiency and AP property of the proposed method. - oai:arXiv.org:2507.02392v2 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Yiyang Hong, Yi Shi, Yi Cai, Tao Xiong - - - Exploring Exponential Runge-Kutta Methods: A Survey - https://arxiv.org/abs/2507.04024 - arXiv:2507.04024v2 Announce Type: replace -Abstract: In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more than a century ago, and exponential integrators, which date back to the 1960s. This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience. - oai:arXiv.org:2507.04024v2 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alessia and\`o, Nicol\`o Cangiotti, Mattia Sensi - - - Degenerate symplectic fixed points and Gromov-Witten invariants - https://arxiv.org/abs/2507.04191 - arXiv:2507.04191v2 Announce Type: replace -Abstract: In this paper we establish a connection between Gromov-Witten invariants and the number of degenerate fixed points of Hamiltonian diffeomorphisms on a closed rational symplectic manifold via deformed Hamiltonian spectral invariants. We prove a new cuplength estimate, in particular including Arnol'd conjecture over complex numbers, for fixed points of Hamiltonian diffeomorphisms on closed rational symplectic manifolds admitting nonzero Gromov-Witten invariants with two point insertions. We extend Schwarz's quantum cuplength to the notion of deformed quantum cuplength for symplectic periods and employ it to estimate the number of fixed points of Hamiltonian diffeomorphisms on monotone symplectic manifolds with nonzero mixed Gromov-Witten invariants. We generalize Givental's symplectic fixed point theorem for toric manifolds to closed rational symplectic manifolds admitting nonzero Gromov-Witten invariants with fixed marked points and one point insertion. - oai:arXiv.org:2507.04191v2 - math.SG - math.AG - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wenmin Gong - - - Retrodicting Chaotic Systems: An Algorithmic Information Theory Approach - https://arxiv.org/abs/2507.04780 - arXiv:2507.04780v2 Announce Type: replace -Abstract: Making accurate inferences about data is a key task in science and mathematics. Here we study the problem of \emph{retrodiction}, inferring past values of a series, in the context of chaotic dynamical systems. Specifically, we are interested in inferring the starting value $x_0$ in the series $x_0,x_1,x_2,\dots,x_n$ given the value of $x_n$, and the associated function $f$ which determines the series as $f(x_i)=x_{i+1}$. Even in the deterministic case this is a challenging problem, due to mixing and the typically exponentially many candidate past values in the pre-image of any given value $x_n$ (e.g., a current observation). We study this task from the perspective of algorithmic information theory, which motivates two approaches: One to search for the `simplest' value in the set of candidates, and one to look for the value in the lowest density region of the candidates. We test these methods numerically on the logistic map, Tent map, Bernoulli map, and Julia/Mandelbrot map, which are well-studied maps in chaos theory. The methods aid in retrodiction by assigning low ranks to candidates which are more likely to be the true starting value. Our approach works well in some parameter and map cases, and outperforms several other retrodiction techniques (each of which fails to outperform random guessing). Nonetheless, the approach is not effective in all cases, and several open problems remain including computational cost and sensitivity to noise. All of these methods are unified through a Gaussian Process (GP) perspective, motivating complexity-based priors for GPs. - oai:arXiv.org:2507.04780v2 - math.DS - nlin.CD - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Kamal Dingle, Boumediene Hamzi, Marcus Hutter, Houman Owhadi - - - Parameter estimation in interacting particle systems on dynamic random networks - https://arxiv.org/abs/2507.06633 - arXiv:2507.06633v2 Announce Type: replace -Abstract: In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of the two connected vertices, while the vertex dynamics does not depend on the edge process. Our goal is to estimate the underlying dynamics from partial information of the process, specifically from snapshots of the total number of edges present. We showcase the effectiveness of our inference method through various numerical results. - oai:arXiv.org:2507.06633v2 - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1103/k8cr-vkkf - Physical Review E 112, 054301 (2025) - Simone Baldassarri, Jiesen Wang - - - $\Gamma$-convergence for nonlocal phase transitions involving the $H^{1/2}$ norm - https://arxiv.org/abs/2507.11054 - arXiv:2507.11054v2 Announce Type: replace -Abstract: We study functionals \begin{equation*} - F_\varepsilon (u) := \lambda_\varepsilon \int_\Omega W(u) \, dx + - \varepsilon \|u\|_{H^{1/2}}^2 \end{equation*} for a double well potential $W$ and the Gagliardo seminorm $\|\cdot\|_{H^{1/2}}$ when $\varepsilon \ln(\lambda_\varepsilon) \rightarrow k$ as $\varepsilon \rightarrow 0^+$ and show compactness in the space of $BV$ functions on $\Omega$ and the $\Gamma$-convergence to the classical surface tension functional. - oai:arXiv.org:2507.11054v2 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tim Heilmann - - - Level sets of prevalent Weierstrass functions - https://arxiv.org/abs/2507.15591 - arXiv:2507.15591v2 Announce Type: replace -Abstract: The $\alpha$-Weierstrass function is defined as $W_g^{\alpha,b}(x) = \sum_{k=0}^{\infty} b^{-\alpha k} g(b^k x)$, where $g$ is a Lipschitz function on the unit circle. For a prevalent $\alpha$-Weierstrass function, we prove that the upper Minkowski dimension of every level set is at most $1-\alpha$, and the Hausdorff dimension of almost every level set equals $1-\alpha$ with respect to its occupation measure. We further demonstrate that the occupation measure of a prevalent $\alpha$-Weierstrass function is absolutely continuous with respect to the Lebesgue measure. Consequently, the result on the Hausdorff dimension of level sets applies to a set of level sets with positive Lebesgue measure. A central tool in our analysis is the Weierstrass embedding. For a sufficiently large dimension $d$, we construct Lipschitz functions $g_0, g_1, \ldots, g_{d-1}$ such that the mapping $x \mapsto \big(W_{g_0}^{\alpha,b}(x), W_{g_1}^{\alpha,b}(x), \ldots, W_{g_{d-1}}^{\alpha,b}(x)\big)$ is $\alpha$-bi-H\"older. We also prove that such an embedding requires at least $1/\alpha$ coordinate functions. - oai:arXiv.org:2507.15591v2 - math.CA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Zolt\'an Buczolich, Antti K\"aenm\"aki, Bal\'azs Maga - - - Exponential mixing of frame flows for three dimensional manifolds of quarter-pinched negative curvature - https://arxiv.org/abs/2508.01593 - arXiv:2508.01593v3 Announce Type: replace -Abstract: For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to a class of torus extensions of Anosov flows, subject to assumptions on the Brin transitivity group and the smoothness of the stable subbundle. Our approach is based on a simplified dynamical model for studying the extension flow, constructed via a Young tower of the underlying Anosov flow. Exponential mixing is then obtained through a strengthened Dolgopyat type estimate on the corresponding transfer operators. - oai:arXiv.org:2508.01593v3 - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/publicdomain/zero/1.0/ - Daofei Zhang - - - On $\boldsymbol{\psi}$-amicable numbers and their generalizations - https://arxiv.org/abs/2508.02318 - arXiv:2508.02318v2 Announce Type: replace -Abstract: In this article, we study the properties of $\psi$-amicable numbers. We prove that their asymptotic density relative to the positive integers is zero. We also propose generalizations of $\psi$-amicable numbers. - oai:arXiv.org:2508.02318v2 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - S. I. Dimitrov - - - Reynolds Lie bialgebras - https://arxiv.org/abs/2508.03507 - arXiv:2508.03507v3 Announce Type: replace -Abstract: In this paper, we establish a bialgebra theory for Reynolds Lie algebras. First we introduce the notion of a quadratic Reynolds Lie algebra and show that it induces an isomorphism from the adjoint representation to the coadjoint representation. Then we introduce the notion of matched pairs, Manin triples and bialgebras for Reynolds Lie algebras, and show that Manin triples, bialgebras and certain matched pairs of Reynolds Lie algebras are equivalent. In particular, we introduce the notion of a Reynolds operator on a quadratic Rota-Baxter Lie algebra which can induce a Reynolds Lie bialgebra naturally. Finally, we introduce the notion of the classical Yang-Baxter equation in a Reynolds Lie algebra whose solutions give rise to Reynolds Lie bialgebras. We also introduce the notion of relative Rota-Baxter operators on a Reynolds Lie algebra and Reynolds pre-Lie algebras, and construct solutions of the classical Yang-Baxter equation in terms of relative Rota-Baxter operators and Reynolds pre-Lie algebras. - oai:arXiv.org:2508.03507v3 - math.RA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shuai Hou, Maxim Goncharov - - - On the sums of rearrangement-invariant quasi-Banach function spaces and their relationship to amalgams - https://arxiv.org/abs/2508.10825 - arXiv:2508.10825v2 Announce Type: replace -Abstract: In this paper we consider the properties of sums of rearrangement-invariant quasi-Banach function spaces, with the focus being on rearrangement-invariance and the Fatou property. In our first main result, we show that the quasinorm of the sum is in many cases equivalent to a rearrangement-invariant quasinorm by providing a weaker version of the Luxemburg-type representation. In our second main result, we show that the sum can be in some cases characterised as a Wiener--Luxemburg amalgam of the two constituent spaces, thus providing a sufficient condition for the sum being a rearrangement-invariant quasi-Banach function space. - oai:arXiv.org:2508.10825v2 - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dalimil Pe\v{s}a - - - Darboux's Theorem in $p$-adic symplectic geometry - https://arxiv.org/abs/2508.15443 - arXiv:2508.15443v3 Announce Type: replace -Abstract: Let $p$ be a prime number. We derive an analog of Moser's Path Method for $p$-adic analytic manifolds and use it to prove a $p$-adic analog of Darboux's Theorem. Using it as a stepping stone we give a classification of second-countable $p$-adic analytic symplectic manifolds in terms of $p$-adic volume. This is a symplectic version of a classical result of Serre in $p$-adic analytic geometry from 1965. We also prove a $p$-adic version of Weinstein's generalization of Darboux's Theorem to neighborhoods of compact manifolds. Finally we find explicitly Darboux's coordinates for the physical models by Ablowitz-Ladik and Salerno of the Discrete Nonlinear Schr\"odinger equation. - Symplectic geometry is deeply connected with classical and quantum mechanics, and a main motivation of this paper is to pursue a $p$-adic version of symplectic geometry following recent developments which incorporate the $p$-adic numbers into mathematical and theoretical physics. - oai:arXiv.org:2508.15443v3 - math.SG - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Luis Crespo, \'Alvaro Pelayo - - - Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights - https://arxiv.org/abs/2508.21409 - arXiv:2508.21409v2 Announce Type: replace -Abstract: We consider in this work the crucial quantity $t_c$ that determines the critical inverse temperature $\beta_c$ in the $q$-state Potts model on sparse rank-1 random graphs where the vertices are equipped with a Pareto weight density $(\tau-1)\,w^{-\tau}\,{\cal X}_{[1,\infty)}(w)$. It is shown in \cite{ref1} that this $t_c$ is the unique positive zero of a function ${\cal K}$ that is obtained by an appropriate combination of the stationarity condition and the criticality condition for the case the external field $B$ equals 0 and that $q\geq3$ and $\tau\geq4$, see \cite{ref1}, Theorem~1.14 and Theorem ~1.21 and their proofs in \cite{ref1}, Section~7.1 and Section~7.3. From the proof of \cite{ref1}, Theorem~1.14, it is seen that ${\cal K}'$ and ${\cal K}''$ also have a unique positive zero, $t_c'$ and $t_c''$, respectively, and $t_c'=t_b$ and $t_c''=t_{\ast}$, where $t_b$ and $t_{\ast}$ are the unique positive zeros of ${\cal F}_0(t)-t\,{\cal F}_0'(t)$ and ${\cal F}_0''(t)$, respectively. Here, ${\cal F}_0(t)=E\,[W(e^{tW}-1)/(E\,[W]\,(e^{tW}+q-1))]$, and $t_c$, $t_b$ and $t_{\ast}$ play a key role in the graphical analysis of \cite{ref1}, Section~5.1 and Figure~1. Furthermore, $\gamma_c=\exp(\beta_c)-1$ and $t_c$ are related according to $\gamma_c=t_c/{\cal F}_0(t_c)$. - We analyse $t_c$, $t_c'$ and $t_c''$ for general real $\tau\geq4$ and general real $q>2$ by an appropriate formulation of their defining equations ${\cal K}(t_c)={\cal K}'(t_c')={\cal K}''(t_c'')=0$. Thus we find, along with the inequality $0<t_c''<t_c'<t_c<\infty$, the simple upper bounds $t_c<2\,{\rm ln}(q-1)$, $t_c'<\frac32\,{\rm ln}(q-1)$, $t_c''<{\rm ln}(q-1)$, as well as certain sharpenings of these simple bounds and counterparts about the large-$q$ behaviour of $t_c$, $t_c$ and $t_c''$. We show that these bounds are sharp in the sense that they hold with equality for the limiting homogeneous case $\tau\to\infty$. - oai:arXiv.org:2508.21409v2 - math-ph - math.MP - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - A. J. E. M. Janssen - - - Finite random iterated function systems do not always satisfy Bowen's formula - https://arxiv.org/abs/2509.02070 - arXiv:2509.02070v2 Announce Type: replace -Abstract: In this paper, we provide a finite random iterated function system satisfying the open set condition, for which the random version of Bowen's formula fails to hold. This counterexample shows that analogous results established for random recursive constructions are not always obtained for random iterated function systems. - oai:arXiv.org:2509.02070v2 - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yuya Arima - - - Moments of density-dependent branching processes and their genealogy - https://arxiv.org/abs/2509.05231 - arXiv:2509.05231v3 Announce Type: replace -Abstract: A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of breaking the branching property. We propose a general approach for studying the genealogy of these models based on moments. Building on a recent work of Bansaye, we show how to compute recursively these moments in a similar spirit to the many-to-few formula in the theory of branching processes. These formulas enable one to deduce the convergence of the genealogy by studying the population density, for which stochastic calculus techniques are available. As a first application of these ideas, we consider a density-dependent branching process started close to a stable equilibrium of the ecological dynamics. We show that, under a finite second moment assumption, its genealogy converges to Kingman's coalescent when the carrying capacity of the population goes to infinity. - oai:arXiv.org:2509.05231v3 - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Mathilde Andr\'e, F\'elix Foutel-Rodier, Emmanuel Schertzer - - - Is the projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_4$ a permutation module? - https://arxiv.org/abs/2509.05805 - arXiv:2509.05805v2 Announce Type: replace -Abstract: We determine the ordinary character of the projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_4$, and answer the question posed in the title. - oai:arXiv.org:2509.05805v2 - math.RT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - 10.1016/j.jalgebra.2025.10.018 - J\"urgen M\"uller - - - A note on higher integrability of projections - https://arxiv.org/abs/2509.06474 - arXiv:2509.06474v2 Announce Type: replace -Abstract: Let $t \in [1,2)$ and $p > 2/(2 - t)$. I construct a $t$-Frostman Borel measure $\mu$ on $[0,1]^{2}$ such that $\pi_{\theta}\mu \notin L^{p}$ for every $\theta \in S^{1}$. This answers a question of Peres and Schlag. - oai:arXiv.org:2509.06474v2 - math.CA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tuomas Orponen - - - Gaussian Copula-Based Outage Performance Analysis of Fluid Antenna Systems: Channel Coefficient- or Envelope-Level Correlation Matrix? - https://arxiv.org/abs/2509.09411 - arXiv:2509.09411v3 Announce Type: replace -Abstract: Gaussian copula has been employed to evaluate the outage performance of Fluid Antenna Systems (FAS), with the covariance matrix reflecting the dependence among multivariate normal random variables (RVs). While prior studies approximate this matrix using the channel coefficient correlation matrix from Jake's model, this work instead employs the channel envelope correlation matrix, motivated by the fact that the multivariate normal RVs are generated by transforming correlated channel envelopes. This raises an open question of whether using the coefficient- or envelope-level correlation matrix yields better accuracy in accessing FAS performance. Toward this end, this paper explores the benefits of using the envelope-level correlation matrix under fully correlated Nakagami-m fading, and develops a method for generating such fading channels for Monte Carlo simulations, which serve as a benchmark for validating the theoretical results. Simulation results confirm the effectiveness of the proposed channel modeling approach and demonstrate the superior accuracy of using the envelope-level correlation matrix, particularly in sparse port deployment and low-outage regime. - oai:arXiv.org:2509.09411v3 - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1109/LWC.2025.3629524 - Rui Xu, Yinghui Ye, Xiaoli Chu, Guangyue Lu, Farshad Rostami Ghadi, Kai-Kit Wong - - - Critical and asymmetric Fourier uniqueness pairs - https://arxiv.org/abs/2509.17600 - arXiv:2509.17600v2 Announce Type: replace -Abstract: Motivated by the recent work of Kulikov, Nazarov, and Sodin, we construct sufficient conditions for discrete subsets of $\mathbb{R}$, which lie between the supercritical and subcritical cases, to constitute Fourier uniqueness pairs. This family of critical uniqueness pairs includes pairs that are strongly asymmetric, stretching beyond those associated with zeros of zeta and L-functions, discovered by Bondarenko, Radchenko, and Seip, and getting arbitrarily close to the classical Shannon--Whittaker uniqueness pair. We also identify a somewhat more restrictive family of strongly asymmetric uniqueness pairs that yield frames and hence Fourier interpolation. - oai:arXiv.org:2509.17600v2 - math.CA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Torgeir Keun Lysen - - - On Pauling's residual entropy estimate for regular graphs with growing degree - https://arxiv.org/abs/2509.20671 - arXiv:2509.20671v2 Announce Type: replace -Abstract: In 1935, Pauling proposed an estimate for the number of Eulerian orientations of a graph in the context of the theoretical behaviour of water ice. The logarithm of the number of Eulerian orientations, normalised by the number of vertices, is called the residual entropy. In an earlier paper, we conjectured that the residual entropy of a sequence of regular graphs of increasing degree was asymptotically equal to Pauling's estimate. Here we prove the conjecture under constraints on the number of short circuits. These constraints hold under weak eigenvalue conditions and apply to sequences of increasing girth and repeated Cartesian products such as hypercubes. - oai:arXiv.org:2509.20671v2 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - M. Hasheminezhad, M. Isaev, B. D. McKay, R-R. Zhang - - - A weak regularity lemma for polynomials - https://arxiv.org/abs/2509.21536 - arXiv:2509.21536v2 Announce Type: replace -Abstract: A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming of having tower-type bounds or worse. In this paper we design a new, weaker regularity lemma with strong bounds. The new regularity lemma in particular provides means to quantitatively study the curves contained in the image of a polynomial map, which is beyond the reach of standard methods. - Applications include strong bounds for a problem of Karam on generalized rank, as well as a new method to obtain upper bounds for fan-in parameters in arithmetic circuits. For example, we show that if the image of a polynomial map $\mathbf{P} \colon \mathbb{F}^n \to \mathbb{F}^m$ of degree $d$ does not contain a line, then $\mathbf{P}$ can be computed by a depth-$4$ arithmetic formula with bottom fan-in at most $d/2$ and top fan-in at most $(2m)^{C(d)}$ (with $C(d)=2^{(1+o(1))d}$). One implication of our work is a certain ``barrier'' to arithmetic circuit lower bounds, in terms of the smallest degree of a polynomial curve contained in the image of the given polynomial map. - oai:arXiv.org:2509.21536v2 - math.CO - cs.CC - math.AC - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Guy Moshkovitz, Dora Woodruff - - - Translates of completely normal elements and the Morgan-Mullen conjecture - https://arxiv.org/abs/2509.23245 - arXiv:2509.23245v2 Announce Type: replace -Abstract: Denote by $\mathbb F_q$ the finite field of order $q$ and by $\mathbb F_{q^n}$ its extension of degree $n$. Some $a\in\mathbb F_{q^n}$ is called primitive if it generates the multiplicative group $\mathbb F_{q^n}^*$ and it is called $q^n/q$-normal if its $\mathbb F_q$-conjugates form an $\mathbb F_q$-basis of $\mathbb F_{q^n}$ if the latter is viewed as an $\mathbb F_q$-vector space. Furthermore, some $a\in\mathbb F_{q^n}$ is called $q^n/q$-completely normal if it is $q^n/q^d$-normal for all $d\mid n$. In this work we prove a new construction of sets of completely normal elements and, we establish, under conditions, the existence of elements that are simultaneously primitive and $q^n/q$-completely normal, covering some yet unresolved cases of a 30-year-old conjecture by Morgan and Mullen. - oai:arXiv.org:2509.23245v2 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Theodoulos Garefalakis, Giorgos Kapetanakis - - - A categorical perspective on non-abelian localization - https://arxiv.org/abs/2509.24009 - arXiv:2509.24009v2 Announce Type: replace -Abstract: In equivariant geometry, a localization (a.k.a., concentration) theorem is typically interpreted as a relationship between the equivariant geometry of a space with a group action and the geometry of its fixed locus. We take a different perspective, that of non-abelian localization: a localization theorem relates the geometry of an algebraic stack that is equipped with a $\Theta$-stratification to the geometry of the centers of this stratification. We establish a ``virtual'' $K$-theoretic non-abelian localization formula, meaning it applies to algebraic derived stacks with perfect cotangent complexes. We also establish a categorical upgrade of this theorem, by introducing a category of ``highest weight $K$-homology cycles'' with respect to the stratification, and relating the category of highest weight cycles on the stack to those on the centers of its $\Theta$-stratification. We apply these results to prove a universal wall-crossing formula, and establish a new finiteness theorem for the cohomology of tautological complexes on the stack of one-dimensional sheaves on an algebraic surface. - oai:arXiv.org:2509.24009v2 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Daniel Halpern-Leistner - - - Computing weighted sheaf cohomology using noncommutative differential modules - https://arxiv.org/abs/2510.02131 - arXiv:2510.02131v2 Announce Type: replace -Abstract: We describe a novel method for computing sheaf cohomology over weighted projective spaces and stacks using exterior algebra and differential module techniques, generalizing an algorithm due to Eisenbud-Fl\o ystad-Schreyer over projective space. - oai:arXiv.org:2510.02131v2 - math.AG - math.AC - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Michael K. Brown, Daniel Erman - - - Equivariant Eilenberg-Watts theorems for locally compact quantum groups - https://arxiv.org/abs/2510.06206 - arXiv:2510.06206v2 Announce Type: replace -Abstract: Given two von Neumann algebras $A$ and $B$, the $W^*$-algebraic Eilenberg-Watts theorem, due to M. Rieffel, asserts that there is a canonical equivalence $\operatorname{Corr}(A,B)\simeq \operatorname{Fun}(\operatorname{Rep}(B), \operatorname{Rep}(A))$ of categories, where $\operatorname{Corr}(A,B)$ denotes the category of all $A$-$B$-correspondences, $\operatorname{Rep}(A)$ is the category of all unital normal $*$-representations of $A$ on Hilbert spaces and $\operatorname{Fun}(\operatorname{Rep}(B), \operatorname{Rep}(A))$ denotes the category of all normal $*$-functors $\operatorname{Rep}(B)\to \operatorname{Rep}(A)$. In this paper, we upgrade the von Neumann algebras $A$ and $B$ with actions $A\curvearrowleft \mathbb{G}$ and $B\curvearrowleft \mathbb{G}$ of a locally compact quantum group $\mathbb{G}$, and we provide several equivariant versions of the $W^*$-algebraic Eilenberg-Watts theorem using the language of module categories. We also prove that for a locally compact quantum group $\mathbb{G}$ with Drinfeld double $D(\mathbb{G})$, the category of unitary $D(\mathbb{G})$-representations is isomorphic to the Drinfeld center of $\operatorname{Rep}(\mathbb{G})$, generalizing a result by Neshveyev-Yamashita from the compact to the locally compact setting. - oai:arXiv.org:2510.06206v2 - math.OA - math.CT - math.QA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Joeri De Ro - - - A probabilistic approach to strong natural boundaries - https://arxiv.org/abs/2510.08717 - arXiv:2510.08717v2 Announce Type: replace -Abstract: We study the local non-extendability of random power series beyond their disk of convergence. We show that random power series formed by independent coefficients which are asymptotically anti-concentrated admit the circle of radius of convergence as strong natural boundary, even in a Nevanlinna sense. Our results extend previous work of Breuer and Simon (2011) for the case of independent coefficients. Our motivation stems from the study of Pad\'e approximants of random power series as a denoising tool. - oai:arXiv.org:2510.08717v2 - math.PR - math.CV - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Stamatis Dostoglou, Petros Valettas - - - Finite element methods for electroneutral multicomponent electrolyte flows - https://arxiv.org/abs/2510.14923 - arXiv:2510.14923v3 Announce Type: replace -Abstract: We present a broad family of high-order finite element algorithms for simulating the flow of electroneutral electrolytes. The governing partial differential equations that we solve are the electroneutral Navier-Stokes-Onsager-Stefan-Maxwell (NSOSM) equations, which model momentum transport, multicomponent diffusion and electrical effects within the electrolyte. Our algorithms can be applied in the steady and transient settings, in two and three spatial dimensions, and under a variety of boundary conditions. Moreover, we allow for the material parameters (e.g. viscosity, diffusivities, thermodynamic factors and density) to be solution-dependent and thermodynamically non-ideal. The flexibility of our approach requires us to address subtleties that arise in the governing equations due to the interplay between boundary conditions and the equation of state. We demonstrate the algorithms in various physical configurations, including (i) electrolyte flow around a microfluidic rotating disk electrode and (ii) the flow in a Hull cell of a cosolvent electrolyte mixture used in lithium-ion batteries. - oai:arXiv.org:2510.14923v3 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Aaron Baier-Reinio, Patrick E. Farrell, Charles W. Monroe - - - Vu's conjecture holds for claw-free graphs - https://arxiv.org/abs/2510.15553 - arXiv:2510.15553v2 Announce Type: replace -Abstract: Given a graph $G$, let $\Delta_2(G)$ denote the maximum number of neighbors any two distinct vertices of $G$ have in common. Vu (2002) proposed that, provided $\Delta_2(G)$ is not too small as a proportion of the maximum degree $\Delta(G)$ of $G$, the chromatic number of $G$ should never be too much larger than $\Delta_2(G)$. We make a first approach towards Vu's conjecture from a structural graph theoretic point of view. We prove that, in the case where $G$ is claw-free, indeed the chromatic number of $G$ is at most $\Delta_2(G)+3$. This is tight, as our bound is met with equality for the line graph of the Petersen graph. Moreover, we can prove this in terms of the more specific parameter that bounds the maximum number of neighbors any two endpoints of some edge of $G$ have in common. Our result may be viewed as a generalization of the classic bound of Vizing (1964) for edge-coloring. - oai:arXiv.org:2510.15553v2 - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Linda Cook, Ross J. Kang, Eileen Robinson, Gabri\"elle Zwaneveld - - - Batch learning equals online learning in Bayesian supervised learning - https://arxiv.org/abs/2510.16892 - arXiv:2510.16892v3 Announce Type: replace -Abstract: Using functoriality of probabilistic morphisms, we prove that sequential and batch Bayesian inversions coincide in supervised learning models with conditionally independent (possibly non-i.i.d.) data \cite{Le2025}. This equivalence holds without domination or discreteness assumptions on sampling operators. We derive a recursive formula for posterior predictive distributions, which reduces to the Kalman filter in Gaussian process regression. For Polish label spaces $\mathcal{Y}$ and arbitrary input sets $\mathcal{X}$, we characterize probability measures on $\mathcal{P}(\mathcal{Y})^{\mathcal{X}}$ via projective systems, generalizing Orbanz \cite{Orbanz2011}. We revisit MacEachern's Dependent Dirichlet Processes (DDP) \cite{MacEachern2000} using copula-based constructions \cite{BJQ2012} and show how to compute posterior predictive distributions in universal Bayesian supervised models with DDP priors. - oai:arXiv.org:2510.16892v3 - math.ST - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - H\^ong V\^an L\^e - - - Comparison of motives with rational coefficients - https://arxiv.org/abs/2510.17194 - arXiv:2510.17194v5 Announce Type: replace -Abstract: The theory of rational motives admits several models, including those of Morel, Beilinson, Ayoub, and Voevodsky. An open question has been the equivalence of Voevodsky's Nisnevich-based $\mathrm{DM}(S, \mathbb{Q})$ with the others, which was only known over excellent and geometrically unibranch base schemes. - In this paper, we prove that modules over rational motivic Eilenberg Maclane spectrum $\mathbf{H}\mathbb{Q}$ is equivalent to Morel/Beilinson/Ayoub's rational motives over any Noetherian semi-normal base scheme $S$. - Our main technical result is a stable motivic equivalence between the free $\mathbb{Q}$-linear spectrum $\mathbb{Q}[\mathbb{S}]$ and the motivic rational Eilenberg MacLane spectrum $\mathbf{H}\mathbb{Q}$. This equivalence is established by reducing the problem to an unstable comparison, where we apply our rational $\mathbb{A}^1$-Dold-Thom theorem, which depends on rational motivic Whitehead theorem that we develop. - As a byproduct, we partially confirm that rational variant of Voevodsky's conjecture that the formation of $\mathbf{H}\mathbb{Q}$ is stable under base change between any Noetherian semi-normal schemes. - oai:arXiv.org:2510.17194v5 - math.AG - math.AT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Bo Zhang - - - On Affine Version of Hom-Lie Algebras - https://arxiv.org/abs/2510.17983 - arXiv:2510.17983v2 Announce Type: replace -Abstract: This paper introduces Hom-type analogues of affine algebraic structures, termed Hom-affgebras. Extending Brzezi\'nski's theory of affgebras and the Hom-algebra framework developed by Hartwig-Larsson-Silvestrov, we define and study Hom-associative, Hom-pre-Lie, and Hom-Lie affgebras, where the classical identities are twisted by an affine self-map. We show how Hom-associative, Hom-pre-Lie, and Hom-Lie affgebras are related to one another. The main focus of this paper is on Hom-Lie affgebras and their fibers. We study the concept of generalized derivations for Hom-Lie algebras, extending the notion of generalized derivations for Lie algebras. We explore the close relationship between Hom-Lie affgebras and such derivations. We show that every Hom-Lie affgebra both determines and is determined by a Hom-Lie algebra together with such a generalized derivation and a constant. Furthermore, we establish that a homomorphism between Lie affgebras corresponds to a homomorphism between their associated Lie fibers along with a constant, and vice versa. - oai:arXiv.org:2510.17983v2 - math.RA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Tarik Anowar, Ripan Saha - - - A Criterion for Perfectoid Purity and the Rationality of Thresholds - https://arxiv.org/abs/2510.19319 - arXiv:2510.19319v2 Announce Type: replace -Abstract: We introduce a new criterion providing a sufficient condition for a hypersurface in an unramified regular local ring to be perfectoid pure. The criterion is formulated in terms of an explicitly computable sequence of integers, called the splitting-order sequence. Our main theorem shows that if all entries of the sequence are at most $p-1$, then the hypersurface is perfectoid pure, and the perfectoid-pure threshold can be computed explicitly from it. As a consequence, we prove that for any regular local ring $R$, the perfectoid pure threshold $\mathrm{ppt}(R,p)$ with respect to $p$ is always a rational number. Moreover, we show that for sufficiently large primes $p$, the cone over a Fermat type Calabi-Yau hypersurface is perfectoid pure, revealing new and unexpected examples of perfectoid pure singularities. Moreover, we show that for sufficiently large primes $p$, the cone over a Fermat type Calabi-Yau hypersurface is perfectoid pure, revealing new and unexpected examples of perfectoid pure singularities. - oai:arXiv.org:2510.19319v2 - math.AG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shou Yoshikawa - - - Distances between non-symmetric convex bodies: optimal bounds up to polylog - https://arxiv.org/abs/2510.20511 - arXiv:2510.20511v2 Announce Type: replace -Abstract: We show that the non-symmetric Banach-Mazur distance between two convex bodies $K_1, K_2 \subseteq \mathbb{R}^n$ satisfies $$ d_{BM}(K_1, K_2) \leq C n \cdot \log^{\alpha} (n+1), $$ for universal constants $C, \alpha > 0$. This improves upon the earlier bound $C n^{4/3} \log^{\alpha} (n+1)$ due to Rudelson. Up to polylogarithmic factors, our estimate is optimal and it also matches the optimal bound in the centrally-symmetric case which is realized in the John position, as proven by Gluskin. The bound above for the Banach-Mazur distance is attained when both bodies are in a ``random isotropic position'', that is, in isotropic position after a random rotation. Our proof is based on an $M$-bound in the isotropic position, which complements E. Milman's $M^*$-bound. In addition, we consider the partial containment distance $d_{PC}(K_1, K_2)$ between two convex bodies $K_1, K_2 \subseteq \mathbb{R}^n$, where the Banach-Mazur requirement to contain $100\%$ of the other body is relaxed to $99\%$-containment. We prove that for any pair of convex bodies $K_1, K_2 \subseteq \mathbb{R}^n$, $$ d_{PC}(K_1, K_2) \leq C \log^{\alpha} (n+1), $$ and that any isotropic position of $K_1$ and $K_2$ yields this polylogarithmic bound for $d_{PC}$. - oai:arXiv.org:2510.20511v2 - math.MG - math.FA - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pierre Bizeul, Boaz Klartag - - - Well-Posedness and Approximation of Weak Solutions to Time Dependent Maxwell's Equations with $L^2$-Data - https://arxiv.org/abs/2510.20752 - arXiv:2510.20752v2 Announce Type: replace -Abstract: We study Maxwell's equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and $L^2$-data. Our first contribution is a direct proof of well-posedness of the first-order weak formulation, including solution existence and uniqueness, an energy identity, and continuous dependence on the data. The argument uses interior-in-time mollification to show uniqueness while avoiding reflection techniques. Existence is via the well-known Galerkin method (cf.~Duvaut and Lions \cite[Eqns.~(4.31)--(4.32), p.~346; Thm.~4.1]{GDuvaut_JLLions_1976a}). For completeness, and to make the paper self-contained, a complete proof has been provided. - Our second contribution is a structure-preserving semi-discrete finite element method based on the N\'ed\'elec/Raviart--Thomas de Rham complex. The scheme preserves a discrete Gauss law for all times and satisfies a continuous-in-time energy identity with stability for nonnegative conductivity. With a divergence-free initialization of the magnetic field (via potential reconstruction or constrained $L^2$ projection), we prove convergence of the semi-discrete solutions to the unique weak solution as the mesh is refined. The analysis mostly relies on projector consistency, weak-* compactness in time-bounded $L^2$ spaces, and identification of time derivatives in dual spaces. - oai:arXiv.org:2510.20752v2 - math.NA - cs.NA - math.AP - physics.comp-ph - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Harbir Antil - - - A Tverberg-type problem of Kalai: Two negative answers to questions of Alon and Smorodinsky, and the power of disjointness - https://arxiv.org/abs/2510.20770 - arXiv:2510.20770v2 Announce Type: replace -Abstract: Let $f_r(d,s_1,\ldots,s_r)$ denote the least integer $n$ such that every $n$-point set $P\subseteq\mathbb{R}^d$ admits a partition $P=P_1\cup\cdots\cup P_r$ with the property that for any choice of $s_i$-convex sets $C_i\supseteq P_i$ $(i\in[r])$ one necessarily has $\bigcap_{i=1}^r C_i\neq\emptyset$, where an $s_i$-convex set means a union of $s_i$ convex sets. A recent breakthrough by Alon and Smorodinsky establishes a general upper bound $f_r(d,s_1,\dots,s_r) = O(dr^2\log r \prod_{i=1}^r s_i\cdot \log(\prod_{i=1}^r s_i).$ Specializing to $r=2$ resolves the problem of Kalai from the 1970s. They further singled out two particularly intriguing questions: whether $f_{2}(2,s,s)$ can be improved from $O(s^2\log s)$ to $O(s)$, and whether $f_r(d,s,\ldots,s)\le Poly(r,d,s)$. We answer both in the negative by showing the exponential lower bound $f_{r}(d,s,\ldots,s)> s^{r}$ for any $r\ge 2$, $s\ge 1$ and $d\ge 2r-2$, which matches the upper bound up to a multiplicative $\log{s}$ factor for sufficiently large $s$. Our construction combines a scalloped planar configuration with a direct product of regular $s$-gon on the high-dimensional torus $(\mathbb{S}^1)^{r-2}$. Perhaps surprisingly, if we additionally require that within each block the $s_i$ convex sets are pairwise disjoint, the picture changes markedly. Let $F_r(d,s_1,\ldots,s_r)$ denote this disjoint-union variant of the extremal function. We show: (1) $F_{2}(2,s,s)=O(s\log s)$ by connecting it to a suitable line-separating function in the plane; (2) when $s$ is large, $F_r(d,s,\ldots,s)$ can be bounded by $O_{r,d}(s^{(1-\frac{1}{2^{d}(d+1)})r+1})$ and $O_{d}(r^{3}\log r\cdot s^{2d+3})$, respectively. This builds on a novel connection between the geometric obstruction and hypergraph Tur\'{a}n numbers, in particular, a variant of the Erd\H{o}s box problem. - oai:arXiv.org:2510.20770v2 - math.CO - cs.CG - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Wenchong Chen, Gennian Ge, Yang Shu, Zhouningxin Wang, Zixiang Xu - - - Explicit surjectivity of Galois representations of products of elliptic curves over function fields - https://arxiv.org/abs/2510.20910 - arXiv:2510.20910v3 Announce Type: replace -Abstract: We prove an explicit surjectivity result for products of non-isotrivial, non-isogenous elliptic curves over a function field of arbitrary characteristic. This is by way of an isogeny degree bound in this setting, generated from bounds for elliptic curves by Griffon--Pazuki, and techniques originated by Serre and Masser--W\"{u}stholz in the number field setting. We apply our result to prove that most members of a family of products of elliptic curves over $\mathbb{Q}$ with no extra endomorphisms have no exceptional primes above a specified constant which depends neither on the elliptic curve factors nor on the dimension of the product. - oai:arXiv.org:2510.20910v3 - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Alina Cojocaru, Frederick Saia - - - Bifurcations of twisted solutions in a continuum limit for the Kuramoto model on nearest neighbor graphs - https://arxiv.org/abs/2510.22663 - arXiv:2510.22663v2 Announce Type: replace -Abstract: We study bifurcations of twisted solutions in a continuum limit (CL) for the Kuramoto model (KM) of identical oscillators defined on nearest neighbor graphs, which may be deterministic dense, random dense or random sparse, when it may have phase-lag. We use the center manifold reduction, which is a standard technique in dynamical systems theory, and prove that the CL suffers bifurcations at which the one-parameter family of twisted solutions becomes unstable and a stable or unstable two-parameter family of modulated twisted solutions that oscillate or not depending on whether the phase-lag exists or not is born. We demonstrate the theoretical results by numerical simulations for the KM on deterministic dense, random dense and random sparse graphs. - oai:arXiv.org:2510.22663v2 - math.DS - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kazuyuki Yagasaki - - - Renormalized Energy and Vortex Interaction in Finsler Ginzburg-Landau Models - https://arxiv.org/abs/2510.23048 - arXiv:2510.23048v2 Announce Type: replace -Abstract: We develop a Finsler Ginzburg--Landau framework for the analysis of vortex interactions in anisotropic superconductors. Within this setting, the Finsler structure encodes directional dependence of the condensate energy, yielding a renormalized energy W_F that governs both equilibrium and dynamics of vortices. We derive the Gamma--limit, establish the analytical structure and stability of W_F, and show that vortex motion follows a Finsler gradient flow exhibiting anisotropic dissipation and drift. This approach provides a unified geometric and physical model for anisotropic superconductivity. - oai:arXiv.org:2510.23048v2 - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Y. Alipour Fakhri - - - Numerical Spectrum Linking: Identification of Governing PDE via Koopman-Chebyshev Approximation - https://arxiv.org/abs/2510.23078 - arXiv:2510.23078v2 Announce Type: replace -Abstract: A numerical framework is proposed for identifying partial differential equations (PDEs) governing dynamical systems directly from their observation data using Chebyshev polynomial approximation. In contrast to data-driven approaches such as dynamic mode decomposition (DMD), which approximate the Koopman operator without a clear connection to differential operators, the proposed method constructs finite-dimensional Koopman matrices by projecting the dynamics onto a Chebyshev basis, thereby capturing both differential and nonlinear terms. This establishes a numerical link between the Koopman and differential operators. Numerical experiments on benchmark dynamical systems confirm the accuracy and efficiency of the approach, underscoring its potential for interpretable operator learning. The framework also lays a foundation for future integration with symbolic regression, enabling the construction of explicit mathematical models directly from data. - oai:arXiv.org:2510.23078v2 - math.NA - cs.NA - eess.SP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Phonepaserth Sisaykeo, Shogo Muramatsu - - - Minimal depth $K$-types for wild double covers and Shimura correspondences - https://arxiv.org/abs/2510.23265 - arXiv:2510.23265v2 Announce Type: replace -Abstract: We construct some Iwahori types, in the sense of Bushnell-Kutzko, for the double cover of an almost simple simply-laced simply-connected Chevalley group $\widetilde{G}$ over any $2$-adic field. These types capture the covering group analog of the Bernstein block of unramified principal series. - We also prove that the associated Hecke algebra essentially admits an Iwahori-Matsumoto (IM) presentation. The complete presentation is obtained for types $A_{r}$, $D_{2r+1}$, $E_{6}$, $E_{7}$; for the other types, some technical obstacles remain. Those Hecke algebras with the complete IM presentation are isomorphic to Iwahori-Hecke algebras of explicit linear Chevalley groups, giving rise to Shimura correspondences. - Along the way, we show that the Iwahori type extends to a hyperspecial maximal compact subgroup $\widetilde{K}\subseteq \widetilde{G}$. This extension has minimal depth among the genuine $\widetilde{K}$-representations and allows us to construct a finite Shimura correspondence, generalizing a result of Savin. - oai:arXiv.org:2510.23265v2 - math.RT - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Edmund Karasiewicz, Shuichiro Takeda - - - Full Benjamin-Feir instability of capillary-gravity Stokes waves in finite depth - https://arxiv.org/abs/2510.23456 - arXiv:2510.23456v2 Announce Type: replace -Abstract: We study the two-dimensional gravity-capillary water waves equations for a fluid of finite depth $\mathtt{h}>0$ under the combined effects of gravity and surface tension $\kappa \geq 0$. We analyze the linear stability and instability of small-amplitude, $2\pi$-periodic Stokes wave solutions, under the effect of longitudinal long-wave perturbations. The corresponding linearized operator has periodic coefficients and a defective zero eigenvalue of multiplicity four. Using Bloch-Floquet theory, we investigate the associated family of periodic eigenvalue problems. For all surface tension values $\kappa \geq 0$ and depths $\mathtt{h} > 0$, we establish the complete splitting of the four eigenvalues near zero when both the wave amplitude and the Floquet parameter are small. Specifically, we rigorously prove that in the regions of unstable depth and capillarity identified formally by Djordjevic-Redekopp and Ablowitz-Segur in the 1970's, the spectrum of the linearized operator near the origin depicts a "figure 8" pattern. - oai:arXiv.org:2510.23456v2 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ting-Yang Hsiao, Alberto Maspero - - - Curvature-based rejection sampling - https://arxiv.org/abs/2510.24537 - arXiv:2510.24537v2 Announce Type: replace -Abstract: The present work introduces curvature-based rejection sampling (CURS). This is a method for sampling from a general class of probability densities defined on Riemannian manifolds. It can be used to sample from any probability density which ``depends only on distance". The idea is to combine the statistical principle of rejection sampling with the geometric principle of volume comparison. CURS is an exact sampling method and (assuming the underlying Riemannian manifold satisfies certain technical conditions) it has a particularly moderate computational cost. The aim of the present work is to show that there are many applications where CURS should be the user's method of choice for dealing with relatively low-dimensional scenarios. - oai:arXiv.org:2510.24537v2 - math.ST - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Isabella Costa Maia, Marco Congedo, Pedro L. C. Rodrigues, Salem Said - - - Kemeny's constant minimization for reversible Markov chains via structure-preserving perturbations - https://arxiv.org/abs/2510.24679 - arXiv:2510.24679v2 Announce Type: replace -Abstract: Kemeny's constant measures the efficiency of a Markov chain in traversing its states. We investigate whether structure-preserving perturbations to the transition probabilities of a reversible Markov chain can improve its connectivity while maintaining a fixed stationary distribution. Although the minimum achievable value for Kemeny's constant can be estimated, the required perturbations may be infeasible. We reformulate the problem as an optimization task, focusing on solution existence and efficient algorithms, with an emphasis to the problem of minimizing Kemeny's constant under sparsity constraints. - oai:arXiv.org:2510.24679v2 - math.NA - cs.NA - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fabio Durastante, Miryam Gnazzo, Beatrice Meini - - - Stochastic Control of Dividends with a Drawdown Penalty - https://arxiv.org/abs/2510.25494 - arXiv:2510.25494v2 Announce Type: replace -Abstract: We consider a diffusion risk model where dividends are paid at rate $U(t) \in [0, u_0]$. We are interested in maximising the dividend payments under a drawdown constraint, that is, we penalise a drawdown size larger than a level $d > 0$. We show that the optimal dividend rate $U(t)$ is either zero or the maximal rate $u_0$ and determine the optimal strategy. Moreover, we derive an explicit expression for the value function by solving a system of differential equations. - oai:arXiv.org:2510.25494v2 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kira Dudziak, Hanspeter Schmidli - - - An explicit formula of the limit of the heat kernel measures on the spheres embedded in $\mathbb {R}^\infty$ - https://arxiv.org/abs/2510.25855 - arXiv:2510.25855v2 Announce Type: replace -Abstract: We show that the heat kernel measures based at the north pole of the spheres $S^{N-1}(\sqrt N)$, with properly scaled radius $\sqrt N$ and adjusted center, converge to a Gaussian measure in $\mathbb R^\infty$, and find an explicit formula for this measure. - oai:arXiv.org:2510.25855v2 - math.PR - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Minh-Luan Doan, Evan O'Dorney - - - Sine Laws with an Anti-Automorphism: A Left-Translation Approach - https://arxiv.org/abs/2511.00019 - arXiv:2511.00019v2 Announce Type: replace -Abstract: Stetk\ae r's matrix method is a useful tool for analyzing functional equations on semigroups involving a homomorphism $\sigma$. However, this method fails when $\sigma$ is an anti-automorphism because the underlying right-regular representation reverses composition order. To resolve this, we introduce a new approach based on a key conjugation identity. Let $J$ denote the operator of composition with $\sigma$; then the identity $J R(\sigma(y)) J = L(y)$ provides the foundation for our method. This identity restores a well-behaved representation via left translations, making the matrix method applicable again. This left-translation approach is illustrated with several concrete examples from matrix groups and symmetric groups. Using this approach, we extend Stetk\ae r's main structural theorem for the generalized sine law to the anti-automorphic setting. For linearly independent solutions, we show that the equation implies a simpler addition law and that the solutions obey the same transformation rules ($f\circ\sigma=\beta f$, etc.) as in the homomorphic case. - oai:arXiv.org:2511.00019v2 - math.GM - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dang Vo Phuc - - - Stochastic representation of solutions for the parabolic Cauchy problem with variable exponent coefficients - https://arxiv.org/abs/2511.00773 - arXiv:2511.00773v2 Announce Type: replace -Abstract: In this work, we prove existence and uniqueness of a bounded viscosity solution for the Cauchy problem of degenerate parabolic equations with variable exponent coefficients. We construct the solution directly using the stochastic representation, then verify it satisfies the Cauchy problem. The corresponding SDE, on the other hand, allows the drift and diffusion coefficients to respond nonlinearly to the current state through the state-dependent variable exponents, and thus, extends the expressive power of classical SDEs to better capture complex dynamics. To validate our theoretical framework, we conduct comprehensive numerical experiments comparing finite difference solutions (Crank-Nicolson on logarithmic grids) with Monte Carlo simulations of the SDE. - oai:arXiv.org:2511.00773v2 - math.AP - cs.NA - math.NA - math.PR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mustafa Avci - - - On the Computability of Finding Capacity-Achieving Codes - https://arxiv.org/abs/2511.01414 - arXiv:2511.01414v2 Announce Type: replace -Abstract: This work studies the problem of constructing capacity-achieving codes from an algorithmic perspective. Specifically, we prove that there exists a Turing machine which, given a discrete memoryless channel $p_{Y|X}$, a target rate $R$ less than the channel capacity $C(p_{Y|X})$, and an error tolerance $\epsilon > 0$, outputs a block code $\mathcal{C}$ achieving a rate at least $R$ and a maximum block error probability below $\epsilon$. The machine operates in the general case where all transition probabilities of $p_{Y|X}$ are computable real numbers, and the parameters $R$ and $\epsilon$ are rational. The proof builds on Shannon's channel coding theorem and relies on an exhaustive search approach that systematically enumerates all codes of increasing block length until a valid code is found. This construction is formalized using the theory of recursive functions, yielding a $\mu$-recursive function $\mathrm{FindCode} : \mathbb{N}^3 \rightharpoonup \mathbb{N}$ that takes as input appropriate encodings of $p_{Y|X}$, $R$, and $\epsilon$, and, whenever $R < C(p_{Y|X})$, outputs an encoding of a valid code. By Kleene's normal form theorem, which establishes the computational equivalence between Turing machines and $\mu$-recursive functions, we conclude that the problem is solvable by a Turing machine. This result can also be extended to the case where $\epsilon$ is a computable real number, while we further discuss an analogous generalization of our analysis when $R$ is computable as well. We note that the assumptions that the probabilities of $p_{Y|X}$, as well as $\epsilon$ and $R$, are computable real numbers cannot be further weakened, since computable reals constitute the largest subset of $\mathbb{R}$ representable by algorithmic means. - oai:arXiv.org:2511.01414v2 - cs.IT - math.IT - math.LO - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Angelos Gkekas, Nikos A. Mitsiou, Ioannis Souldatos, George K. Karagiannidis - - - On Generalized Characters Whose Values on Nonidentity Elements are Sums of at Most Two Roots of Unity - https://arxiv.org/abs/2511.01782 - arXiv:2511.01782v3 Announce Type: replace -Abstract: A character of a finite group having degree $n$ takes values which may be expressed as sums of $n$ or fewer roots of unity. In this note, we prove a result which describes the irreducible constituents of generalized characters on abelian groups whose values on nonidentity elements are expressible as sums of two or fewer roots of unity. In Section 4, we apply our main result to obtain information about the connectivity of prime graphs for groups admitting such characters. - oai:arXiv.org:2511.01782v3 - math.GR - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Christopher Herbig - - - On the Boltzmann-Fermi-Dirac Equation for Hard Potential: Global Existence and Uniqueness, Gaussian Lower Bound, and Moment Estimates - https://arxiv.org/abs/2511.02273 - arXiv:2511.02273v2 Announce Type: replace -Abstract: In this paper, we study the global existence and uniqueness, Gaussian lower bound, and moment estimates in the spatially homogeneous Boltzmann equation for Fermi-Dirac particles for hard potential ($0\leq \gamma\leq 2$) with angular cutoff $b$. Our results extend classical results to the Boltzmann-Fermi-Dirac setting. In detail, (1) we show existence, uniqueness, and $L^1_2$ stability of global-in-time solutions of the Boltzmann-Fermi-Dirac equation. (2) Assuming the solution is not a saturated equilibrium, we prove creation of a Gaussian lower bound for the solution. (3) We prove creation and propagation of $L^1$ polynomial and exponential moments of the solution under additional assumptions on the angular kernel $b$ and $0<\gamma\leq 2$. (4) Finally, we show propagation of $L^\infty$ Gaussian and polynomial upper bounds when $b$ is constant and $0<\gamma\leq 1$. - oai:arXiv.org:2511.02273v2 - math.AP - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gayoung An, Sungbin Park - - - Restricted Liouville Operator for the study of Non-Analytic Dynamics within the Disk - https://arxiv.org/abs/2511.02305 - arXiv:2511.02305v2 Announce Type: replace -Abstract: The study of Koopman and Liouville operators over reproducing kernel Hilbert spaces (RKHSs) has been gaining considerable interest over the past decade. In particular, these operators represent nonlinear dynamical systems, and through the study of these operators, methods of system identification and approximation can be derived through the exploitation of the linearity of these systems. The resulting algorithms, such as Dynamic Mode Decompositions, can then make predictions about the finite-dimensional nonlinear dynamics through a linear model in infinite dimensions. However, considering bounded and densely defined Koopman and Liouville operators over RKHSs often restricts the dynamics to those whose smoothness or analyticity matches that of the functions within that space. To circumvent this limitation, this manuscript introduces the Restricted Liouville Operator over the Hardy space on unit disc, which will allow for a wider class of dynamics (non-analytic or non-smooth) than available. - oai:arXiv.org:2511.02305v2 - math.FA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Sushant Pokhriyal, Joel A Rosenfeld - - - Fiedler-Based Characterization and Identification of Leaders in Semi-Autonomous Networks - https://arxiv.org/abs/2511.02317 - arXiv:2511.02317v2 Announce Type: replace -Abstract: This paper addresses the problem of identifying leader nodes in semi-autonomous consensus networks from observed agent dynamics. Using the grounded Laplacian formulation, we derive spectral conditions that ensure the components of the Fiedler vector associated with leader and follower nodes are distinct. Building on the foundation, we emply the notion of relative tempo from prio works as an observable quantity that relates agents' steady-state velocities to the Fiedler vector. This relationship enables the development of a data-driven algorithm that reconstructs the Fiedler vector - and consequently identifies the leader set - using only steady-state velocity measurements, without requiring knowledge of the network topology. The proposed approach is validated through nuerical examples, demonstrating how spectral properties and relative tempo measurements can be combined to reveal hidden leadership structures in consensus networks. - oai:arXiv.org:2511.02317v2 - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Evyatar Matmon, Daniel Zelazo - - - Discretization and convergence of the ballistic Benamou-Brenier formulation of the porous medium and Burgers equations - https://arxiv.org/abs/2511.02662 - arXiv:2511.02662v2 Announce Type: replace -Abstract: We study the discretization, convergence, and numerical implementation of recent reformulations of the quadratic porous medium equation (multidimensional and anisotropic) and Burgers' equation (one-dimensional, with optional viscosity), as forward in time variants of the Benamou-Brenier formulation of optimal transport. This approach turns those evolution problems into global optimization problems in time and space, of which we introduce a discretization, one of whose originalities lies in the harmonic interpolation of the densities involved. We prove that the resulting schemes are unconditionally stable w.r.t. the space and time steps, and we establish a quadratic convergence rate for the dual PDE solution, under suitable assumptions. We also show that the schemes can be efficiently solved numerically using a proximal splitting method and a global space-time fast Fourier transform, and we illustrate our results with numerical experiments. - oai:arXiv.org:2511.02662v2 - math.NA - cs.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Jean-Marie Mirebeau, Erwan Stampfli - - - A Christ-Fefferman type approach to the one sided maximal operator - https://arxiv.org/abs/2511.02741 - arXiv:2511.02741v2 Announce Type: replace -Abstract: In this paper, an approach to the one sided maximal function in the spirit of the Christ-Fefferman proof for the strong type weighted estimates of the maximal function is provided. As applications of that approach, we provide an alternative proof of the sharp weighted estimate for the one sided maximal function that was settled by one of us and de la Torre, a one sided two weight bumps counterpart of a result of P\'erez and Rela, and also one sided counterparts of some very recent mixed weak type results due to Sweeting. - oai:arXiv.org:2511.02741v2 - math.CA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Francisco J. Mart\'in-Reyes, Israel P. Rivera-R\'ios, Pablo Rodr\'iguez-Padilla - - - An accelerated primal-dual flow for linearly constrained multiobjective optimization - https://arxiv.org/abs/2511.02751 - arXiv:2511.02751v2 Announce Type: replace -Abstract: In this paper, we propose a continuous-time primal-dual approach for linearly constrained multiobjective optimization problems. A novel dynamical model, called accelerated multiobjective primal-dual flow, is presented with a second-order equation for the primal variable and a first-order equation for the dual variable. It can be viewed as an extension of the accelerated primal-dual flow by Luo [arXiv:2109.12604, 2021] for the single objective case. To facilitate the convergence rate analysis, we introduce a new merit function, which motivates the use of the feasibility violation and the objective gap to measure the weakly Pareto optimality. By using a proper Lyapunov function, we establish the exponential decay rate in the continuous level. After that, we consider an implicit-explicit scheme, which yields an accelerated multiobjective primal-dual method with a quadratic subproblem, and prove the sublinear rates of the feasibility violation and the objective gap, under the convex case and the strongly convex case, respectively. Numerical results are provided to demonstrate the performance of the proposed method. - oai:arXiv.org:2511.02751v2 - math.OC - cs.NA - math.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hao Luo, Qiaoyuan Shu, Xinmin Yang - - - An explicit construction of Kaleidocycles by elliptic theta functions - https://arxiv.org/abs/2308.04977 - arXiv:2308.04977v3 Announce Type: replace-cross -Abstract: We consider the configuration space of ordered points on the two-dimensional sphere that satisfy a specific system of quadratic equations. We construct periodic orbits in this configuration space using elliptic theta functions and show that they simultaneously satisfy semi-discrete analogues of mKdV and sine-Gordon equations. The configuration space we investigate corresponds to the state space of a linkage mechanism known as the Kaleidocycle, and the constructed orbits describe the characteristic motion of the Kaleidocycle. A key consequence of our construction is the proof that Kaleidocycles exist for any number of tetrahedra greater than five. Our approach is founded on the relationship between the deformation of spatial curves and integrable systems, offering an intriguing example where an integrable system is explicitly solved to generate an orbit in the space of real solutions to polynomial equations defined by geometric constraints. - oai:arXiv.org:2308.04977v3 - nlin.SI - cs.RO - math.DG - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Shizuo Kaji, Kenji Kajiwara, Shota Shigetomi - - - Variable Selection and Minimax Prediction in High-dimensional Functional Linear Model - https://arxiv.org/abs/2310.14419 - arXiv:2310.14419v5 Announce Type: replace-cross -Abstract: High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each predictor is a random element in an infinite-dimensional function space, and the number of functional predictors p can potentially be ultra-high. Assuming that each of the unknown coefficient functions belongs to some reproducing kernel Hilbert space (RKHS), we regularize the fitting of the model by imposing a group elastic-net type of penalty on the RKHS norms of the coefficient functions. We show that our loss function is Gateaux sub-differentiable, and our functional elastic-net estimator exists uniquely in the product RKHS. Under suitable sparsity assumptions and a functional version of the irrepresentable condition, we derive a non-asymptotic tail bound for variable selection consistency of our method. Allowing the number of true functional predictors $q$ to diverge with the sample size, we also show a post-selection refined estimator can achieve the oracle minimax optimal prediction rate. The proposed methods are illustrated through simulation studies and a real-data application from the Human Connectome Project. - oai:arXiv.org:2310.14419v5 - stat.ME - math.ST - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.5705/ss.202025.0151 - Statistica Sinica (2028) - Xingche Guo, Yehua Li, Tailen Hsing - - - Individualizing Glioma Radiotherapy Planning by Optimization of Data and Physics-Informed Discrete Loss - https://arxiv.org/abs/2312.05063 - arXiv:2312.05063v4 Announce Type: replace-cross -Abstract: Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-specific progressions is essential for effective therapies. Current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. This "one size fits all" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. We present the GliODIL framework, which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging, leveraging a Fisher-Kolmogorov type physics model to describe tumor growth. This is achieved through the newly introduced method of Optimizing the Discrete Loss, where both data and physics-based constraints are softly assimilated into the solution. Our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. By blending data-driven techniques with physics-based constraints, GliODIL enhances recurrence prediction in radiotherapy planning, challenging traditional uniform margins and strict adherence to the Fisher-Kolmogorov partial differential equation model, which is adapted for complex cases. - oai:arXiv.org:2312.05063v4 - physics.med-ph - cs.NA - math.NA - q-bio.QM - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Michal Balcerak, Jonas Weidner, Petr Karnakov, Ivan Ezhov, Sergey Litvinov, Petros Koumoutsakos, Tamaz Amiranashvili, Ray Zirui Zhang, John S. Lowengrub, Bene Wiestler, Bjoern Menze - - - Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing - https://arxiv.org/abs/2406.18651 - arXiv:2406.18651v3 Announce Type: replace-cross -Abstract: A quantum generalized divergence by definition satisfies the data-processing inequality; as such, the relative decrease in such a divergence under the action of a quantum channel is at most one. This relative decrease is formally known as the contraction coefficient of the channel and the divergence. Interestingly, there exist combinations of channels and divergences for which the contraction coefficient is strictly less than one. Furthermore, understanding the contraction coefficient is fundamental for the study of statistical tasks under privacy constraints. To this end, here we establish upper bounds on contraction coefficients for the hockey-stick divergence under privacy constraints, where privacy is quantified with respect to the quantum local differential privacy (QLDP) framework, and we fully characterize the contraction coefficient for the trace distance under privacy constraints. With the machinery developed, we also determine an upper bound on the contraction of both the Bures distance and quantum relative entropy relative to the normalized trace distance, under QLDP constraints. Next, we apply our findings to establish bounds on the sample complexity of quantum hypothesis testing under privacy constraints. Furthermore, we study various scenarios in which the sample complexity bounds are tight, while providing order-optimal quantum channels that achieve those bounds. Lastly, we show how private quantum channels provide fairness and Holevo information stability in quantum learning settings. - oai:arXiv.org:2406.18651v3 - quant-ph - cs.CR - cs.IT - cs.LG - math.IT - stat.ML - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1109/TIT.2025.3527859 - IEEE Transactions on Information Theory, Volume 71, Issue 3, Pages 1851--1873, March 2025 - Theshani Nuradha, Mark M. Wilde - - - Anomalous Dynamics of Superparamagnetic Colloidal Microrobots with Tailored Statistics - https://arxiv.org/abs/2412.13960 - arXiv:2412.13960v4 Announce Type: replace-cross -Abstract: Living organisms have developed advanced motion strategies for efficient space exploration, serving as inspiration for the movements of microrobots. These real-life strategies often involve anomalous dynamics displaying random movement patterns that deviate from Brownian motion. Despite their biological inspiration, autonomous stochastic navigation strategies of current microrobots remain much less versatile than those of their living counterparts. Supported by theoretical reasoning, this work demonstrates superparamagnetic colloidal microrobots with fully customizable stochastic dynamics displaying the entire spectrum of anomalous diffusion, from subdiffusion to superdiffusion, across statistically significant spatial and temporal scales (covering at least two decades). By simultaneously tuning microrobots' step-length distribution and, critically, their velocity autocorrelation function with magnetic fields, fundamental anomalous dynamics are reproduced with tailored properties mimicking L\'evy walks and fractional Brownian motion. These findings pave the way for programmable microrobotic systems that replicate optimal stochastic navigation strategies found in nature for applications in medical robotics and environmental remediation. - oai:arXiv.org:2412.13960v4 - cond-mat.soft - cond-mat.stat-mech - math-ph - math.MP - physics.data-an - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1002/smll.202506538 - Small, e06538 (2025) - Alessia Gentili, Rainer Klages, Giorgio Volpe - - - Beyond Covariance Matrix: The Statistical Complexity of Private Linear Regression - https://arxiv.org/abs/2502.13115 - arXiv:2502.13115v2 Announce Type: replace-cross -Abstract: We study the statistical complexity of private linear regression under an unknown, potentially ill-conditioned covariate distribution. Somewhat surprisingly, under privacy constraints the intrinsic complexity is \emph{not} captured by the usual covariance matrix but rather its $L_1$ analogues. Building on this insight, we establish minimax convergence rates for both the central and local privacy models and introduce an Information-Weighted Regression method that attains the optimal rates. - As application, in private linear contextual bandits, we propose an efficient algorithm that achieves rate-optimal regret bounds of order $\sqrt{T}+\frac{1}{\alpha}$ and $\sqrt{T}/\alpha$ under joint and local $\alpha$-privacy models, respectively. Notably, our results demonstrate that joint privacy comes at almost no additional cost, addressing the open problems posed by Azize and Basu (2024). - oai:arXiv.org:2502.13115v2 - cs.LG - cs.AI - cs.CR - math.ST - stat.ML - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fan Chen, Jiachun Li, Alexander Rakhlin, David Simchi-Levi - - - Dicke subsystems are entangled - https://arxiv.org/abs/2502.18574 - arXiv:2502.18574v3 Announce Type: replace-cross -Abstract: We show that all reduced states of nonproduct symmetric Dicke states of arbitrary number of qudits are genuinely multipartite entangled, and of nonpositive partial transpose with respect to any subsystem. - oai:arXiv.org:2502.18574v3 - quant-ph - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Szil\'ard Szalay, P\'eter Ny\'ari - - - Anomalies of Coset Non-Invertible Symmetries - https://arxiv.org/abs/2503.00105 - arXiv:2503.00105v3 Announce Type: replace-cross -Abstract: Anomalies of global symmetries provide important information on the quantum dynamics. We show the dynamical constraints can be organized into three classes: genuine anomalies, fractional topological responses, and integer responses that can be realized in symmetry-protected topological (SPT) phases. Coset symmetry can be present in many physical systems including quantum spin liquids, and the coset symmetry can be a non-invertible symmetry. We introduce twists in coset symmetries, which modify the fusion rules and the generalized Frobenius-Schur indicators. We call such coset symmetries twisted coset symmetries, and they are labeled by the quadruple $(G,K,\omega_{D+1},\alpha_D)$ in $D$ spacetime dimensions where $G$ is a group and $K\subset G$ is a discrete subgroup, $\omega_{D+1}$ is a $(D+1)$-cocycle for group $G$, and $\alpha_{D}$ is a $D$-cochain for group $K$. We present several examples with twisted coset symmetries using lattice models and field theory, including both gapped and gapless systems (such as gapless symmetry-protected topological phases). We investigate the anomalies of general twisted coset symmetry, which presents obstructions to realizing the coset symmetry in (gapped) symmetry-protected topological phases. We show that finite coset symmetry $G/K$ becomes anomalous when $G$ cannot be expressed as the bicrossed product $G=H\Join K$, and such anomalous coset symmetry leads to symmetry-enforced gaplessness in generic spacetime dimensions. We illustrate examples of anomalous coset symmetries with $A_5/\mathbb{Z}_2$ symmetry, with realizations in lattice models. - oai:arXiv.org:2503.00105v3 - cond-mat.str-el - hep-th - math.QA - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Po-Shen Hsin, Ryohei Kobayashi, Carolyn Zhang - - - Quantization of nonlinear non-Hamiltonian systems - https://arxiv.org/abs/2503.06939 - arXiv:2503.06939v3 Announce Type: replace-cross -Abstract: Several important dynamical systems are in $\mathbb{R}^2$, defined by the pair of differential equations $(x',y')=(f(x,y),g(x,y))$. A question of fundamental importance is how such systems might behave quantum mechanically. In developing quantum theory, Dirac and others realized that classical Hamiltonian systems can be mapped to their quantum counterparts via canonical quantization. The resulting quantum dynamics is always physical, characterized by completely-positive and trace-preserving evolutions in the Schr\"{o}dinger picture. However, whether non-Hamiltonian systems can be quantized systematically while respecting the same physical requirements has remained a long-standing problem. Here we resolve this question when $f(x,y)$ and $g(x,y)$ are arbitrary polynomials. By leveraging open-systems theory, we prove constructively that every polynomial system admits a physical generator of time evolution in the form of a Lindbladian. We call our method cascade quantization, and demonstrate its power by analyzing several paradigmatic examples of nonlinear dynamics such as bifurcations, noise-activated spiking, and Li\'{e}nard systems. In effect, our method can quantize any classical system whose $f(x,y)$ and $g(x,y)$ are analytic with arbitrary precision. More importantly, cascade quantization is exact. This means restrictive system properties usually assumed in the literature to facilitate quantization, such as weak nonlinearity, rotational symmetry, or semiclassical dynamics, can all be dispensed with by cascade quantization. We also highlight the advantages of cascade quantization over existing proposals, by weighing it against examples from the variational paradigm using Lagrangians, as well as non-variational approaches. - oai:arXiv.org:2503.06939v3 - quant-ph - math-ph - math.MP - nlin.AO - nlin.CD - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - 10.1103/l54l-sff5 - Phys. Rev. E 112, 054206 (2025) - Andy Chia, Wai-Keong Mok, Leong-Chuan Kwek, Changsuk Noh - - - Lagrangian multiforms and dispersionless integrable systems - https://arxiv.org/abs/2503.22615 - arXiv:2503.22615v2 Announce Type: replace-cross -Abstract: We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservation laws of linearly degenerate PDEs in 3D, and (b) in the context of Gibbons-Tsarev equations governing hydrodynamic reductions of heavenly type equations in 4D. - oai:arXiv.org:2503.22615v2 - nlin.SI - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - 10.1007/s11005-025-02016-w - Lett Math Phys 115, 125 (2025) - Evgeny V. Ferapontov, Mats Vermeeren - - - A Proof-Theoretic Approach to the Semantics of Classical Linear Logic (Technical Report) - https://arxiv.org/abs/2504.08349 - arXiv:2504.08349v3 Announce Type: replace-cross -Abstract: Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of all contexts that can be used to prove it (e.g. phase semantics) or by assigning meaning directly to proofs (e.g. coherence spaces). - This work proposes a different perspective on assigning meaning to proofs by adopting a proof-theoretic perspective. More specifically, we employ base-extension semantics (BeS) to characterise proofs through the notion of base support. - Recent developments have shown that BeS is powerful enough to capture proof-theoretic notions in structurally rich logics such as intuitionistic linear logic. In this paper, we extend this framework to the classical case, presenting a proof-theoretic approach to the semantics of the multiplicative-additive fragment of linear logic (MALL). - oai:arXiv.org:2504.08349v3 - cs.LO - math.LO - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Victor Barroso-Nascimento, Ekaterina Piotrovskaya, Elaine Pimentel - - - Reactive power flow optimization in AC drive systems - https://arxiv.org/abs/2504.10360 - arXiv:2504.10360v2 Announce Type: replace-cross -Abstract: This paper explores a limit avoidance approach in the case of input (modulation) and output (current) constraints with the aim of enhancing system availability of AC drives. Drawing on the observation that, in a certain range of reactive power, there exists a trade-off between current and modulation magnitude, we exploit this freedom and define a constrained optimization problem. We propose two approaches, one in the form of an activation-function which drives the reactive power set-point towards safety, and an approach which uses online feedback optimization to set the reactive power dynamically. Both methods compromise reactive power tracking accuracy for increased system robustness. Through a high fidelity simulation, we compare the benefits of the two methods, highlighting their effectiveness in industrial applications. - oai:arXiv.org:2504.10360v2 - eess.SY - cs.SY - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Sanjay Chandrasekaran, Catalin Arghir, Pieder Joerg, Florian Doerfler, Silvia Mastellone - - - Aerial Active STAR-RIS-assisted Satellite-Terrestrial Covert Communications - https://arxiv.org/abs/2504.16146 - arXiv:2504.16146v2 Announce Type: replace-cross -Abstract: An integration of satellites and terrestrial networks is crucial for enhancing performance of next generation communication systems. However, the networks are hindered by the long-distance path loss and security risks in dense urban environments. In this work, we propose a satellite-terrestrial covert communication system assisted by the aerial active simultaneous transmitting and reflecting reconfigurable intelligent surface (AASTAR-RIS) to improve the channel capacity while ensuring the transmission covertness. Specifically, we first derive the minimal detection error probability (DEP) under the worst condition that the Warden has perfect channel state information (CSI). Then, we formulate an AASTAR-RIS-assisted satellite-terrestrial covert communication optimization problem (ASCCOP) to maximize the sum of the fair channel capacity for all ground users while meeting the strict covert constraint, by jointly optimizing the trajectory and active beamforming of the AASTAR-RIS. Due to the challenges posed by the complex and high-dimensional state-action spaces as well as the need for efficient exploration in dynamic environments, we propose a generative deterministic policy gradient (GDPG) algorithm, which is a generative deep reinforcement learning (DRL) method to solve the ASCCOP. Concretely, the generative diffusion model (GDM) is utilized as the policy representation of the algorithm to enhance the exploration process by generating diverse and high-quality samples through a series of denoising steps. Moreover, we incorporate an action gradient mechanism to accomplish the policy improvement of the algorithm, which refines the better state-action pairs through the gradient ascent. Simulation results demonstrate that the proposed approach significantly outperforms important benchmarks. - oai:arXiv.org:2504.16146v2 - eess.SP - cs.IT - cs.NI - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Chuang Zhang, Geng Sun, Jiahui Li, Jiacheng Wang, Ruichen Zhang, Dusit Niyato, Shiwen Mao, Tony Q. S. Quek - - - Surmise for random matrices' level spacing distributions beyond nearest-neighbors - https://arxiv.org/abs/2504.20134 - arXiv:2504.20134v2 Announce Type: replace-cross -Abstract: Correlations between energy levels can help distinguish whether a many-body system is of integrable or chaotic nature. The study of short-range and long-range spectral correlations generally involves quantities which are very different, unless one uses the $k$-th nearest neighbor ($k$NN) level spacing distributions. For nearest-neighbor (NN) spectral spacings, the distribution in random matrices is well captured by the Wigner surmise. This well-known approximation, derived exactly for a 2$\times$2 matrix, is simple and satisfactorily describes the NN spacings of larger matrices. There have been attempts in the literature to generalize Wigner's surmise to further away neighbors. However, as we show, the current proposal in the literature fails to accurately capture numerical data. Using the known variance of the distributions from random matrix theory, we propose a corrected surmise for the $k$NN spectral distributions. This surmise better characterizes spectral correlations while retaining the simplicity of Wigner's surmise. We test the predictions against numerical results and show that the corrected surmise is systematically more accurate at capturing data from random matrices. Using the XXZ spin chain with random on-site disorder, we illustrate how these results can be used as a refined probe of many-body quantum chaos for both short- and long-range spectral correlations. - oai:arXiv.org:2504.20134v2 - quant-ph - cond-mat.dis-nn - cond-mat.stat-mech - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - 10.1088/1751-8121/ae15ca - J. Phys. A: Math. Theor. 58 445206 (2025) - Ruth Shir, Pablo Martinez-Azcona, Aur\'elia Chenu - - - A data-driven framework for team selection in Fantasy Premier League - https://arxiv.org/abs/2505.02170 - arXiv:2505.02170v2 Announce Type: replace-cross -Abstract: Fantasy football is a billion-dollar industry with millions of participants. Under a fixed budget, managers select squads to maximize future Fantasy Premier League (FPL) points. This study formulates lineup selection as data-driven optimization and develops deterministic and robust mixed-integer linear programs that choose the starting eleven, bench, and captain under budget, formation, and club-quota constraints (maximum three players per club). The objective is parameterized by a hybrid scoring metric that combines realized FPL points with predictions from a linear regression model trained on match-performance features identified using exploratory data analysis techniques. The study benchmarks alternative objectives and cost estimators, including simple and recency-weighted averages, exponential smoothing, autoregressive integrated moving average (ARIMA), and Monte Carlo simulation. Experiments on the 2023/24 Premier League season show that ARIMA with a constrained budget and a rolling window yields the most consistent out-of-sample performance; weighted averages and Monte Carlo are also competitive. Robust variants improve some objectives but are not uniformly superior. The framework provides transparent decision support for fantasy roster construction and extends to FPL chips, multi-week rolling-horizon transfer planning, and week-by-week dynamic captaincy. - oai:arXiv.org:2505.02170v2 - cs.CE - cs.AI - cs.LG - math.OC - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Danial Ramezani, Tai Dinh - - - A Theoretical Framework for Grokking: Interpolation followed by Riemannian Norm Minimisation - https://arxiv.org/abs/2505.20172 - arXiv:2505.20172v2 Announce Type: replace-cross -Abstract: We study the dynamics of gradient flow with small weight decay on general training losses $F: \mathbb{R}^d \to \mathbb{R}$. Under mild regularity assumptions and assuming convergence of the unregularised gradient flow, we show that the trajectory with weight decay $\lambda$ exhibits a two-phase behaviour as $\lambda \to 0$. During the initial fast phase, the trajectory follows the unregularised gradient flow and converges to a manifold of critical points of $F$. Then, at time of order $1/\lambda$, the trajectory enters a slow drift phase and follows a Riemannian gradient flow minimising the $\ell_2$-norm of the parameters. This purely optimisation-based phenomenon offers a natural explanation for the \textit{grokking} effect observed in deep learning, where the training loss rapidly reaches zero while the test loss plateaus for an extended period before suddenly improving. We argue that this generalisation jump can be attributed to the slow norm reduction induced by weight decay, as explained by our analysis. We validate this mechanism empirically on several synthetic regression tasks. - oai:arXiv.org:2505.20172v2 - cs.LG - math.OC - stat.ML - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Etienne Boursier, Scott Pesme, Radu-Alexandru Dragomir - - - All fractional Shapiro steps in the RSJ model with two Josephson harmonics - https://arxiv.org/abs/2505.20502 - arXiv:2505.20502v2 Announce Type: replace-cross -Abstract: Synchronization between the internal dynamics of the superconducting phase in a Josephson junction (JJ) and an external ac signal is a fundamental physical phenomenon, manifesting as constant-voltage Shapiro steps in the current-voltage characteristic. Mathematically, this phase-locking effect is captured by the Resistively Shunted Junction (RSJ) model, an important example of a nonlinear dynamical system. The standard RSJ model considers an overdamped JJ with a sinusoidal (single-harmonic) current-phase relation (CPR) in the current-driven regime with a monochromatic ac component. While this model predicts only integer Shapiro steps, the inclusion of higher Josephson harmonics is known to generate fractional Shapiro steps. In this paper, we show that only two Josephson harmonics in the CPR are sufficient to produce all possible fractional Shapiro steps within the RSJ framework. Using perturbative methods, we analyze the amplitudes of these fractional steps. Furthermore, by introducing a phase shift between the two Josephson harmonics, we reveal an asymmetry between positive and negative fractional steps - a signature of the Josephson diode effect. - oai:arXiv.org:2505.20502v2 - cond-mat.supr-con - cond-mat.mes-hall - math-ph - math.DS - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pavel N. Tsarev, Yakov V. Fominov - - - New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes - https://arxiv.org/abs/2506.01432 - arXiv:2506.01432v3 Announce Type: replace-cross -Abstract: We present new quantum algorithms for estimating homological invariants, specifically Betti and persistent Betti numbers, of a simplicial complex given through structured classical data. Our approach efficiently constructs block-encodings of (persistent) Laplacians, enabling estimation via stochastic rank methods with complexity polylogarithmic in the number of simplices across both sparse and dense regimes. - Unlike prior spectral algorithms that suffer when Betti numbers are small, we introduce homology tracking and property testing techniques achieving exponential speedups under natural sparsity and structure assumptions. We also formulate homology triviality and equivalence testing as property testing problems, giving nearly linear-time quantum algorithms when the boundary rank is large. A cohomological formulation further yields rank-independent testing and polylog-time manipulation of $r$-cocycles via block-encoded projections. These results open a new direction in quantum topological data analysis and demonstrate provable quantum advantages in computing topological invariants. - oai:arXiv.org:2506.01432v3 - quant-ph - cs.CC - cs.CG - cs.DS - math.AT - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Junseo Lee, Nhat A. Nghiem - - - Generalised wavefunction coefficients and acyclonesto-cosmohedra - https://arxiv.org/abs/2507.09736 - arXiv:2507.09736v2 Announce Type: replace-cross -Abstract: Scattering amplitudes of $\operatorname{tr}(\phi^3)$ theory can be encoded as the canonical form of the Stasheff associahedron. Similarly, the flat-space wavefunction coefficients of the same theory are captured by the recently proposed cosmohedron, a non-simple polytope associated to the Stasheff associahedron; unitarity and locality of the amplitudes and wavefunction coefficients are then encoded in the factorisation properties of faces of these polytopes. In this paper, we argue that these desirable properties of the Stasheff associahedron are shared by a wider class of polytopes called acyclonestohedra and generalise the cosmohedron construction to arbitrary acyclonestohedra. - Acyclonestohedra are generalisations of Stasheff associahedra and graph associahedra defined on the data of a partially ordered set or, more generally, an acyclic realisable matroid on a building set. When the acyclonestohedron is associated to a partially ordered set, it may be interpreted as arising from Chan-Paton-like factors that are only (cyclically) partially ordered, rather than (cyclically) totally ordered as for the ordinary open string. In this paper, we argue that the canonical forms of acyclonestohedra encode scattering-amplitude-like objects that factorise onto themselves, thereby extending recent results for graph associahedra, and construct truncations of acyclonestohedra into acyclonesto-cosmohedra whose canonical forms may be interpreted as encoding a generalisation of the cosmological wavefunction coefficients. As a byproduct, we provide evidence that acyclonesto-cosmohedra can be obtained as sections of graph cosmohedra. - oai:arXiv.org:2507.09736v2 - hep-th - math.CO - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1088/1751-8121/ae1b4e - Stefan Forcey, Ross Glew, Hyungrok Kim - - - Quantum variational calculus on a lattice - https://arxiv.org/abs/2508.02628 - arXiv:2508.02628v2 Announce Type: replace-cross -Abstract: We solve the long-standing problem of variational calculus on a noncommutative space or spacetime for a significant class of models with trivial jet bundle. Our approach entails a quantum version of the Anderson variational double complex $\Omega(J^\infty)$ and includes Euler-Lagrange equations and a partial Noether's theorem. We show in detail how this works for a free field on a $\Bbb Z^m$ lattice regarded as a discrete noncommutative geometry, obtaining the Klein-Gordon equation for a scalar field, including with a general metric and gauge field background, as the Euler-Lagrange equations of motion for an action. In the case of a flat metric we also obtain an exactly on-shell conserved stress-energy tensor and Noether charges for a scalar field on the lattice and modified energy-momentum relations. - oai:arXiv.org:2508.02628v2 - hep-th - gr-qc - math.QA - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shahn Majid, Francisco Sim\~ao - - - Flat connections at infinity on knot surgery manifolds - https://arxiv.org/abs/2509.05270 - arXiv:2509.05270v2 Announce Type: replace-cross -Abstract: $\rm SL(2,\mathbb{C})$ Chern-Simons theory on a closed 3-manifold is one of the most interesting, yet tractable examples of a QFT. On one hand, its non-perturbative structure is not yet fully understood; on the other, the mathematical structure turns out to be very rich. In this work we explore the new phenomenon of flat connections at infinity on various knot surgery manifolds. Such flat connections can be understood as asymptotic ends in the non-compact moduli space of flat $\rm SL(2,\mathbb{C})$ connections. We focus on the examples of $\pm 1/r$-surgeries on torus, twist and some double twist knot complements in $S^3$. Surprisingly, our findings suggest that flat connections at infinity are abundant even for simple low-crossing knot surgeries. We therefore believe that their presence would shed light on the resurgent nature of the path integral. - oai:arXiv.org:2509.05270v2 - hep-th - math-ph - math.AT - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Aditya Dwivedi, Archana Maji, Dmitry Noshchenko, Ramadevi Pichai - - - Integrable Spherical Brane Model at Large $N$ - https://arxiv.org/abs/2509.23869 - arXiv:2509.23869v2 Announce Type: replace-cross -Abstract: We study one of the simplest integrable two-dimensional quantum field theories with a boundary: $N$ free non-compact scalars in the bulk, constrained non-linearly on the boundary to lie on an $(N-1)$-sphere of radius $1/\sqrt{g}$. The $N=1$ case reduces to the single-channel Kondo problem, for $N=2$ the model describes dissipative Coulomb charging in quantum dots, and larger $N$ is analogous to higher-spin impurity or multi-channel scenarios. Adding a boundary magnetic field -- a linear boundary coupling to the scalars -- enriches the model's structure while preserving integrability. Lukyanov and Zamolodchikov (2004) conjectured an expansion for the boundary free energy on the infinite half-cylinder in powers of the magnetic field. Using large-$N$ saddle-point techniques, we confirm their conjecture to next-to-leading order in $1/N$. Renormalization of the subleading solution turns out to be highly instructive, and we connect it to the RG running of $g$ studied by Giombi and Khanchandani (2020). - oai:arXiv.org:2509.23869v2 - hep-th - cond-mat.mes-hall - cond-mat.str-el - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mohsen Gheisarieha, Ramtin M. Yazdi, Arash Arabi Ardehali - - - Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branch - https://arxiv.org/abs/2510.03888 - arXiv:2510.03888v2 Announce Type: replace-cross -Abstract: We find an intriguing relation between the chiral algebra and the mixed Hodge structure of the Coulomb branch of four dimensional $\mathcal{N} = 2$ superconformal field theories. We identify the space of irreducible characters of the $\mathcal{N} = 4$ $SU(N)$ chiral algebra $\mathbb{V}[\mathcal{T}_{SU(N)}]$ by analytically computing the Wilson line Schur index, and imposing modular invariance. We further establish a map from the $\mathbb{V}[\mathcal{T}_{SU(N)}]$ characters to the characters of the $\mathcal{T}_{p, N}$ chiral algebra. We extract the pure part of the mixed Hodge polynomial $PH_c$ of the Coulomb branch compactified on a circle, and prove that $PH_c$ encodes the representation theory of $\mathbb{V}[\mathcal{T}_{SU(N)}]$. We expect this to be a new entry of the 4D mirror symmetry framework. - oai:arXiv.org:2510.03888v2 - hep-th - math-ph - math.MP - math.RT - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yutong Li, Yiwen Pan, Wenbin Yan - - - An efficient spectral Poisson solver for the nirvana-III code: the shearing-box case with vertical vacuum boundary conditions - https://arxiv.org/abs/2510.10070 - arXiv:2510.10070v2 Announce Type: replace-cross -Abstract: The stability of a differentially rotating fluid subject to its own gravity is a problem with applications across wide areas of astrophysics--from protoplanetary discs (PPDs) to entire galaxies. The shearing box formalism offers a conceptually simple framework for studying differential rotation in the local approximation. Aimed at self-gravitating, and importantly, vertically stratified PPDs, we develop two novel methods for solving Poisson's equation in the framework of the shearing box with vertical vacuum boundary conditions (BCs). Both approaches naturally make use of multi-dimensional fast Fourier transforms for computational efficiency. While the first one exploits the linearity properties of the Poisson equation, the second, which is slightly more accurate, consists of finding the adequate discrete Green's function (in Fourier space) adapted to the problem at hand. To this end, we have revisited the method proposed by Vico et al. (2016) and have derived an analytical Green's function satisfying the shear-periodic BCs in the plane as well as vacuum BCs, vertically. Our spectral method demonstrates excellent accuracy, even with a modest number of grid points, and exhibits third-order convergence. It has been implemented in the NIRVANA-III code, where it exhibits good scalability up to 4096 CPU cores, consuming less than 6% of the total runtime. This was achieved through the use of P3DFFT, a fast Fourier Transform library that employs pencil decomposition, overcoming the scalability limitations inherent in libraries using slab decomposition. We have introduced two novel spectral Poisson solvers that guarantees high accuracy, performance, and intrinsically support vertical vacuum boundary conditions in the shearing-box framework. Our solvers enable high-resolution local studies involving self-gravity, such as MHD simulations of gravito-turbulence or gravitational fragmentation. - oai:arXiv.org:2510.10070v2 - astro-ph.IM - math-ph - math.MP - physics.comp-ph - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - S. Rendon Restrepo, O. Gressel - - - Large-$N$ limit of $O(N)^3$-invariant general sextic tensor model - https://arxiv.org/abs/2510.19646 - arXiv:2510.19646v2 Announce Type: replace-cross -Abstract: We study a sextic tensor model where the interaction terms are given by all $O(N)^3$-invariant bubbles. The class of invariants studied here is thus a larger one that the class of the $U(N)^3$-invariant sextic tensor model. We implement the large $N$ limit mechanism for this general model and we explicitly identify the dominant graphs in the $1/N$ expansion. This class of dominant graphs contains tadpole graphs, melonic graphs but also new types of tensor graphs. Our analysis adapts the tensorial intermediate field method, previously applied only to the prismatic interaction, to all connected sextic interactions except the wheel interaction, which we treat separately using a cycle analysis. - oai:arXiv.org:2510.19646v2 - hep-th - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gaetan Bardy, Thomas Krajewski, Thomas Muller, Adrian Tanasa - - - Universal decay of (conditional) mutual information in gapped pure- and mixed-state quantum matter - https://arxiv.org/abs/2510.22867 - arXiv:2510.22867v2 Announce Type: replace-cross -Abstract: For spin and fermionic systems in any spatial dimension, we establish that the superpolynomial decay behavior of mutual information and conditional mutual information is a universal property of gapped pure- and mixed-state phases, i.e., all systems in such a phase possess this property if one system in this phase possesses this property. We further demonstrate that the (conditional) mutual information indeed decays superpolynomially in a large class of phases, including chiral phases. As a byproduct, we sharpen the notion of mixed-state phases. - oai:arXiv.org:2510.22867v2 - cond-mat.str-el - cond-mat.quant-gas - math-ph - math.MP - quant-ph - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jinmin Yi, Kangle Li, Chuan Liu, Zixuan Li, Liujun Zou - - - Bridging the Gap between Empirical Welfare Maximization and Conditional Average Treatment Effect Estimation in Policy Learning - https://arxiv.org/abs/2510.26723 - arXiv:2510.26723v2 Announce Type: replace-cross -Abstract: The goal of policy learning is to train a policy function that recommends a treatment given covariates to maximize population welfare. There are two major approaches in policy learning: the empirical welfare maximization (EWM) approach and the plug-in approach. The EWM approach is analogous to a classification problem, where one first builds an estimator of the population welfare, which is a functional of policy functions, and then trains a policy by maximizing the estimated welfare. In contrast, the plug-in approach is based on regression, where one first estimates the conditional average treatment effect (CATE) and then recommends the treatment with the highest estimated outcome. This study bridges the gap between the two approaches by showing that both are based on essentially the same optimization problem. In particular, we prove an exact equivalence between EWM and least squares over a reparameterization of the policy class. As a consequence, the two approaches are interchangeable in several respects and share the same theoretical guarantees under common conditions. Leveraging this equivalence, we propose a regularization method for policy learning. The reduction to least squares yields a smooth surrogate that is typically easier to optimize in practice. At the same time, for many natural policy classes the inherent combinatorial hardness of exact EWM generally remains, so the reduction should be viewed as an optimization aid rather than a universal bypass of NP-hardness. - oai:arXiv.org:2510.26723v2 - stat.ML - cs.LG - econ.EM - math.ST - stat.ME - stat.TH - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Masahiro Kato - - - The Skolem Problem in rings of positive characteristic - https://arxiv.org/abs/2510.27603 - arXiv:2510.27603v2 Announce Type: replace-cross -Abstract: We show that the Skolem Problem is decidable in finitely generated commutative rings of positive characteristic. More precisely, we show that there exists an algorithm which, given a finite presentation of a (unitary) commutative ring $\mathcal{R} = \mathbb{Z}_{/T}[X_1, \ldots, X_n]/I$ of characteristic $T > 0$, and a linear recurrence sequence $(\gamma_n)_{n \in \mathbb{N}} \in \mathcal{R}^{\mathbb{N}}$, determines whether $(\gamma_n)_{n \in \mathbb{N}}$ contains a zero term. Our proof is based on two recent results: Dong and Shafrir (2025) on the solution set of S-unit equations over $p^e$-torsion modules, and Karimov, Luca, Nieuwveld, Ouaknine, and Worrell (2025) on solving linear equations over powers of two multiplicatively independent numbers. Our result implies, moreover, that the zero set of a linear recurrence sequence over a ring of characteristic $T = p_1^{e_1} \cdots p_k^{e_k}$ is effectively a finite union of $p_i$-normal sets in the sense of Derksen (2007). - oai:arXiv.org:2510.27603v2 - cs.LO - math.NT - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Ruiwen Dong, Doron Shafrir - - - Single-Sided Black Holes in Double-Scaled SYK Model and No Man's Island - https://arxiv.org/abs/2511.01978 - arXiv:2511.01978v2 Announce Type: replace-cross -Abstract: We study a single-sided black hole with an end-of-the-world (EoW) brane behind the horizon in the double-scaled SYK (DSSYK). The new Hamiltonian is a deformation of the original DSSYK Hamiltonian with an extra exponential wormhole length operator, which leads to a new chord diagram rule. The boundary algebra is defined as generated by the new Hamiltonian and boundary matter. There is an alternative but equivalent definition with a $q$-coherent state due to a nontrivial isomorphism of the vN algebra of DSSYK. This isomorphism induces a unitary equivalence, which yields a surprising result that the boundary algebra of a single-sided black hole in DSSYK has a non-trivial commutant and is a type II$_1$ vN factor. It follows that the full bulk reconstruction from the boundary is impossible, and there is a ``no man's island" behind the horizon in the semiclassical JT limit. Inspired by the EoW brane, we construct a family of matter-brane states with an arbitrary number of matter chords and behaving like an EoW brane. They exactly solve the full spectrum of DSSYK. - We take different ways to understand the nontrivial commutant. We show that the commutant is complex on chord number basis and thus non-geometric. In the semiclassical JT limit, the commutant becomes the canonical purification of the boundary algebra and claims the no man's island. In the context of Hawking radiation after Page time, the unitary equivalence is interpreted as encoding the canonical purification into the old Hawking radiation, and the no man's island has the same essence as the island. Including the exponential wormhole length operator independently, the boundary algebra is extended to all bounded operators and reconstructs the no man's island. This can be regarded as a different choice for the definition of boundary algebra. This type I$_\infty$ algebra is closely related to the EoW brane in Kourkoulou-Maldacena. - oai:arXiv.org:2511.01978v2 - hep-th - math-ph - math.MP - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xuchen Cao, Ping Gao - - - Measuring the Intrinsic Dimension of Earth Representations - https://arxiv.org/abs/2511.02101 - arXiv:2511.02101v2 Announce Type: replace-cross -Abstract: Within the context of representation learning for Earth observation, geographic Implicit Neural Representations (INRs) embed low-dimensional location inputs (longitude, latitude) into high-dimensional embeddings, through models trained on geo-referenced satellite, image or text data. Despite the common aim of geographic INRs to distill Earth's data into compact, learning-friendly representations, we lack an understanding of how much information is contained in these Earth representations, and where that information is concentrated. The intrinsic dimension of a dataset measures the number of degrees of freedom required to capture its local variability, regardless of the ambient high-dimensional space in which it is embedded. This work provides the first study of the intrinsic dimensionality of geographic INRs. Analyzing INRs with ambient dimension between 256 and 512, we find that their intrinsic dimensions fall roughly between 2 and 10 and are sensitive to changing spatial resolution and input modalities during INR pre-training. Furthermore, we show that the intrinsic dimension of a geographic INR correlates with downstream task performance and can capture spatial artifacts, facilitating model evaluation and diagnostics. More broadly, our work offers an architecture-agnostic, label-free metric of information content that can enable unsupervised evaluation, model selection, and pre-training design across INRs. - oai:arXiv.org:2511.02101v2 - cs.LG - cs.IT - math.IT - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Arjun Rao, Marc Ru{\ss}wurm, Konstantin Klemmer, Esther Rolf - - - In Situ Training of Implicit Neural Compressors for Scientific Simulations via Sketch-Based Regularization - https://arxiv.org/abs/2511.02659 - arXiv:2511.02659v2 Announce Type: replace-cross -Abstract: Focusing on implicit neural representations, we present a novel in situ training protocol that employs limited memory buffers of full and sketched data samples, where the sketched data are leveraged to prevent catastrophic forgetting. The theoretical motivation for our use of sketching as a regularizer is presented via a simple Johnson-Lindenstrauss-informed result. While our methods may be of wider interest in the field of continual learning, we specifically target in situ neural compression using implicit neural representation-based hypernetworks. We evaluate our method on a variety of complex simulation data in two and three dimensions, over long time horizons, and across unstructured grids and non-Cartesian geometries. On these tasks, we show strong reconstruction performance at high compression rates. Most importantly, we demonstrate that sketching enables the presented in situ scheme to approximately match the performance of the equivalent offline method. - oai:arXiv.org:2511.02659v2 - cs.LG - cs.AI - cs.CE - cs.NA - math.NA - Thu, 06 Nov 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Cooper Simpson, Stephen Becker, Alireza Doostan -